Quantum Computing Research Archive

We map the computational phase transition boundary in binary compressed sensing and identify a regime where D-Wave's quantum annealer recovers signals in a region where all tested classical methods fail, including Approximate Message Passing (AMP), which achieves the Bayes-optimal recovery threshold asymptotically for Gaussian matrices. In 19,775 experiments (n in {32, 64}, nine classical solvers, two D-Wave modes), we find that quantum annealing recovers sparse binary signals in the relaxation gap -- the regime below the Donoho-Tanner l1 phase transition where the l0 solution exists but convex relaxations fail. At n=32, k=5, m/n=0.19, D-Wave achieves 7% exact recovery while AMP and eight other solvers score 0% across 250 combined trials (Fisher exact p=0.018). At n=64, embedding overhead limits the QPU, but D-Wave's hybrid solver remains competitive with AMP. Energy landscape analysis reveals that the QUBO ground state contains the true signal, but incorrect solutions occupy shallower local basins that trap classical search -- a structure consistent with quantum tunneling dynamics. To our knowledge, this constitutes preliminary finite-size evidence that quantum annealing succeeds in a narrow regime where all tested classical methods, including the Bayes-optimal AMP, fail within a well-characterized combinatorial inference problem. Confirmation at larger n, higher trial counts, and with stronger classical controls remains an open problem.

A rigorous characterization of the information content of any highest-spin three-fermion wave function is presented. It is based upon a formal decomposition of the wave function into a finite set of fixed invariants, called shapes, whose sole purpose is to satisfy the Pauli principle, and a variable part, constituting the bosonic excitations of these invariants, that provides its physical content. As an example, this decomposition is applied to a benchmark-quality approximate wave function of the lowest-energy quartet electronic state of the lithium atom. This wave function, which comprises hundreds of basis functions, is reduced to eleven shape blocks, only five of which are numerically significant. Such a compact characterization is a generic example of the appearance of superselection rules in configuration space, and provides a qualitative aid in the search for robust few-particle entangled states.

Haar random states are fundamental objects in quantum information theory and quantum computing. We study the density matrix resulting from sampling t copies of a d -dimensional quantum state according to the Haar measure on the orthogonal group. In particular, we analytically compute its spectral decomposition. This allows us to compute exactly the trace distance between t -copies of a real Haar random state and t -copies of a complex Haar random state. Using this we show a lower-bound on the approximation parameter of real-valued state t -designs and improve the lower-bound on the number of copies required for imaginarity testing.

Dynamical Lie algebras (DLAs) have emerged as a valuable tool in the study of parameterized quantum circuits, helping to characterize both their expressiveness and trainability. In particular, the absence or presence of barren plateaus (BPs) – flat regions in parameter space that prevent the efficient training of variational quantum algorithms – has recently been shown to be intimately related to quantities derived from the associated DLA.In this work, we investigate DLAs for the quantum approximate optimization algorithm (QAOA), one of the most studied variational quantum algorithms for solving graph MaxCut and other combinatorial optimization problems. While DLAs for QAOA circuits have been studied before, existing results have either been based on numerical evidence, or else correspond to DLA generators specifically chosen to be universal for quantum computation on a subspace of states. We initiate an analytical study of barren plateaus and other statistics of QAOA algorithms, and give bounds on the dimensions of the corresponding DLAs and their centers for general graphs. We then focus on the n -vertex cycle and complete graphs. For the cycle graph we give an explicit basis, identify its decomposition into the direct sum of a 2 -dimensional center and a semisimple component isomorphic to n − 1 copies of s u ( 2 ) . We give an explicit basis for this isomorphism, and a closed-form expression for the variance of the cost function, proving the absence of BPs. For the complete graph we prove that the dimension of the DLA is O ( n 3 ) and give an explicit basis for the DLA.

We propose an efficient classical algorithm to estimate the Neural Tangent Kernel (NTK) associated with a broad class of quantum neural networks. These networks consist of arbitrary unitary operators belonging to the Clifford group interleaved with parametric gates given by the time evolution generated by an arbitrary Hamiltonian belonging to the Pauli group. The proposed algorithm leverages a key insight: the average over the distribution of initialization parameters in the NTK definition can be exactly replaced by an average over just four discrete values, chosen such that the corresponding parametric gates are Clifford operations. This reduction enables an efficient classical simulation of the circuit. Combined with recent results establishing the equivalence between wide quantum neural networks and Gaussian processes [Girardi et al., Comm. Math. Phys. 406, 92 (2025); Melchor Hernandez et al., Ann. Henri Poincaré (2025)], our method enables efficient computation of the expected output of wide, trained quantum neural networks, and therefore shows that such networks cannot achieve quantum advantage.

The availability of certain entangled resource states (catalyst states) can enhance the rate of converting several less entangled states into fewer highly entangled states in a process known as catalytic entanglement concentration (EC). Here, we extend catalytic EC from pure states to mixed states and numerically benchmark it against non-catalytic EC and distillation in the presence of state-preparation errors and operational errors. Furthermore, we analyse the re-usability of catalysts in the presence of such errors. To do this, we introduce a novel recipe for determining the positive-operator valued measurements (POVM) required for EC transformations, which allows for making tradeoffs between the number of communication rounds and the number of auxiliary qubits required. We find that in the presence of low operational errors and depolarising noise, catalytic EC can provide better rates than distillation and non-catalytic EC.

Quantum computing experiments have made remarkable progress in demonstrating key components of error-corrected quantum computing, a prerequisite for scalable quantum computation. While we anticipate the near-term arrival of early fault-tolerant quantum hardware capable of a million reliable quantum operations, the cost of preparing low-noise “magic resource states,” which are necessary for performing universal quantum computation, presents a formidable challenge. The recently proposed partially fault-tolerant architecture based on a space-time efficient analog rotation (STAR) approach attempts to address this challenge by using postselection to prepare low-noise, arbitrary small-angle magic states. Its proposed physical implementation, however, assumes fixed qubit connectivity, resulting in implementation costs closer to leading fully fault-tolerant approaches. In this work, we propose the transversal STAR architecture and co-design it with neutral-atom quantum hardware, deriving explicit and significant savings in logical layout, time, and space overhead. Through detailed circuit-level simulations, we derive the logical noise model for surface-code-based transversal STAR gadgets and verify their composability. At its limit, the transversal STAR architecture with neutral atoms can efficiently simulate local Hamiltonians with a total simulation volume exceeding 600, defined as the product of the number of logical qubits and Hamiltonian evolution timescales. Achieving this limit would require approximately 10 000 physical qubits at a physical error rate of 10 − 3 . This is equivalent to a fully fault-tolerant computation requiring over 10 6 – 10 7 T gates and a potential > 100 × saving on space-time volume for equivalent simulation over current, state-of-the-art protocols. Finally, we extend the transversal STAR architecture to high-rate quantum low-density parity-check codes, demonstrating how a limited set of highly parallel transversal Clifford gates and generalized small-angle magic injection can be utilized for effective quantum simulation. We anticipate that the co-designed transversal STAR architecture could substantially reduce the physical resources necessary for early fault-tolerant quantum simulation at the megaquop scale.

Typical security proofs for quantum key distribution (QKD) rely on having some model for the devices, with the security guarantees implicitly relying on the values of various parameters of the model, such as dark count rates or detector efficiencies. Hence to deploy QKD in practice, we must establish how to certify or characterize the model parameters of a manufacturer’s QKD devices. We present a rigorous framework for analyzing such procedures, laying out concrete requirements for both the security proofs and the certification or characterization procedures. In doing so, we describe various forms of conclusions that can and cannot be validly drawn from such procedures, addressing some potential misconceptions. We also discuss connections to composable security frameworks and some technical aspects that remain to be resolved in that direction.

Protecting qubits from perturbations is a central challenge in quantum computing. Topological superconductors with separated Majorana bound states (MBSs) provide a strong form of protection that only depends on the locality of perturbations. While the link between MBS separation, robust degeneracy, and protected braiding is well understood in noninteracting systems, recent experimental progress in short quantum-dot-based Kitaev chains highlights the need to establish these connections rigorously for interacting systems. We do this by defining MBSs from many-body ground states and show how their locality constrains their coupling to an environment. This, in turn, quantifies the protection of the energy degeneracy and the feasibility of non-abelian braiding.

Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains challenging due to the exponential growth of Hilbert space dimension and rapid spreading of entanglement. In this work, we introduce Fourier neural operators (FNOs) as an efficient, accurate, and scalable framework for nonequilibrium quantum dynamics. Parameterized in Fourier space, FNO naturally captures temporal correlations and remains minimally dependent on discretization of time. We demonstrate the versatility of FNO through three complementary learning paradigms: reconstructing effective Floquet Hamiltonians, predicting expectation values of local observables, and learning quantum information spreading. For each learning task, FNO achieves remarkable accuracy, while attaining a significant speedup, compared to exact numerical methods. Moreover, FNO possesses capabilities beyond that of conventional methods, such as predicting all local observables from a subset of measurements without information about the Hamiltonian, as well as extrapolating beyond the time window provided by training data, enabling access to observables and operator-spreading dynamics that might be beyond the coherence time. By employing a spatially local basis, we argue that the computational cost of FNOs scales only polynomially with the system size. Our results establish FNO as a versatile and scalable computation framework that integrates numerical simulations and experimental data seamlessly, with direct implications for extracting meaningful physics from measurements by near-term quantum computers.

The sixth-generation wireless networks are envisioned to deliver ubiquitous, seamless, and intelligent connectivity that reaches far beyond the limits of terrestrial infrastructure. Non-terrestrial networks (NTNs) are central to this vision, extending coverage to underserved regions, remote terrain, and disaster zones that terrestrial deployment cannot economically reach. However, NTN architecture faces numerous limitations: severe path loss over long distances, long propagation delays, large and time-varying Doppler shifts, limited visibility windows, and tight on-board energy and computing budgets. Semantic communication (SemCom), which conveys the meaning of data rather than its raw bit-level representation, is unusually well matched to these conditions: extreme compression rate for task-oriented eases bandwidth scarcity, deep joint source-channel coding prevents the cliff effect due to low signal-to-noise ratio, and generative-AI reconstructs content from sparse cues that survive rain-faded or blocked links. This observation, that each NTN limitation maps onto a SemCom property that addresses it, motivates our survey. We first walk through the NTN limitations one by one, pairing each with the SemCom design choices that complement it, then we organize the literature along three axes: the NTN platform, the semantic methodology, and the supporting techniques, and follow this with platform-by-platform deep dives on satellite-centric, UAV/HAPS-centric, and integrated SAGIN systems. The survey concludes by identifying open research problems, gaps in existing standards, and future directions, including the application of foundation models, energy-aware scheduling, and quantum-assisted SemCom for deep space communication.

We propose an erasure conversion scheme on the | e ⟩ − | f ⟩ and | g ⟩ − | f ⟩ qubits in integer fluxonium qubits (IFQs), which are both first-order insensitive to 1 / f flux noise. The | e ⟩ − | f ⟩ transition is identical to that of a usual fluxonium qubit and hence is expected to have excellent coherence time, while the | g ⟩ − | f ⟩ transition is additionally protected from the energy relaxation by the parity symmetry. The dominant error in both qubits arises due to the energy relaxation: from | e ⟩ to | g ⟩ in the e-f qubit and from | f ⟩ to | e ⟩ in the g-f qubit. Such errors can be treated as erasure events, and their efficient detection improves the performance of quantum error-correcting codes. We consider a protocol for such erasure conversion based on the dispersive readout. Our main finding is that, with proper circuit parameter choice, carefully designed gate sets, and the integration of erasure conversion, IFQs promise highly effective coherence times.

Dynamical decoupling is a central technique in quantum computing for actively suppressing decoherence and systematic imperfections through sequences of single-qubit operations. Conventional sequences typically aim to completely freeze system dynamics, often resulting in long protocols whose length scales exponentially with system size. In this work, we introduce a general framework for constructing time-optimal, selectively tailored sequences that remove only specific local interactions. By combining techniques from graph coloring and classical coding theory, our approach enables compact and hardware-tailored sequences across diverse qubit platforms, efficiently canceling undesired Hamiltonian terms while preserving target interactions. This opens up broad applications in quantum computing and simulation. At the core of our method is a mapping between dynamical decoupling sequence design and error-detecting codes, which allows us to leverage powerful coding-theoretic tools to construct customized sequences. To overcome exponential overheads, we exploit symmetries in colored interaction hypergraphs, extending graph-coloring strategies to arbitrary many-body Hamiltonians. We demonstrate the effectiveness of our framework through concrete examples, including compact sequences that suppress residual ZZ and ZZZ interactions in superconducting qubits and Heisenberg exchange coupling in spin qubits. We also show how it enables Hamiltonian engineering by simulating the anisotropic Kitaev honeycomb model using only isotropic Heisenberg interactions.

Abstract Room-temperature (RT) solid-state quantum emitters are essential for building practical and scalable quantum communication systems, yet their application has been critically hindered by the slow operational speeds of corresponding modulation technologies. In this work, we overcome this key performance bottleneck. We demonstrate a quantum key distribution (QKD) system using a single defect in hexagonal boron nitride (hBN) with dynamic polarization encoding at a 40 MHz clock rate, an order of magnitude faster than previous demonstrations with similar sources. Implementing the B92 protocol, our system yields a secure key rate of 7 kbps in the finite-key regime with a quantum bit error rate of 6.49%, establishing a new performance benchmark for RT single-photon QKD. Furthermore, to chart a path beyond the limits of direct transmission, we present the first quantitative performance analysis of hBN spin-defects as quantum repeater nodes. Overall, our high-speed experimental demonstration, supported by a foundational analysis of the system architecture, suggests that hBN defects represent a promising and technically feasible platform for scalable, quantum communication.

Dynamic circuits use real-time outcomes of mid-circuit measurements, processed by a classical controller, to adapt subsequent operations during circuit execution. This additional flexibility over static circuits comes at a price. Mid-circuit measurements are typically slower and noisier than unitary gates. Furthermore, classical feedforward requires exchanging information between the quantum processor (QPU) and the classical controller, introducing latency that erodes the practical performance of dynamic circuits. We propose a compile-time optimization framework that reduces the use of classical controls in dynamic circuits while preserving their semantics. At its core, the framework uses a static analysis that symbolically executes the circuit by propagating classical information alongside the quantum state. By combining this classical-quantum information with the Probabilistic Circuit Model extended with probabilistic controls that emulate classical feedforward, we obtain an intermediate probabilistic representation of the dynamic circuit. In this representation, mid-circuit measurements and classically controlled operations can be removed or rewritten as purely unitary operations and probabilistic components. Compared to existing compile-time optimizations that target only mid-circuit measurements, our method applies to a broader class of dynamic circuits expressible in modern quantum programming languages. We evaluated our framework on randomly generated dynamic circuits, achieving about 50% classical feedforward reduction and even higher reductions in favorable settings.

The Frauchiger–Renner paradox derives an inconsistency when quantum theory is used to describe the use of itself, by means of a scenario where agents model other agents quantumly and reason about each other's knowledge. We observe that logical contextuality (à la Hardy) is the key ingredient of the FR paradox, and we provide a stronger paradox based on the strongly contextual GHZ–Mermin scenario. In contrast to the FR paradox, this GHZ–FR paradox neither requires post-selection nor any reasoning by observers who are modelled quantumly. If one accepts the universality of quantum theory including superobservers, we propose a natural extension of Peres's dictum to resolve these extended Wigner's friend paradoxes.

Variational quantum computing offers a powerful framework with applications across diverse fields such as quantum chemistry, machine learning, and optimization. However, its scalability is hindered by the exponential concentration of the loss function, known as the barren plateau problem. While significant progress has been made and prior work has separately analyzed barren plateaus in unitary and noisy settings, their combined impact remains poorly understood, largely due to limitations in conventional Lie-algebraic approaches. In this work, we introduce an analytical framework based on non-negative matrix theory that enables the description of the variance in layered noisy quantum circuits with arbitrary noise channels. This approach enables the derivation of exact expressions in the deep-circuit regime, uncovering the complex interplay between unitary layers and noise. Notably, we identify a noise-induced absorption mechanism—a phenomenon absent in purely unitary dynamics—which provides new insight into how noise shapes circuit behavior. We further present a controlled convergence analysis, establishing general lower bounds on the variance of both deep and shallow circuits. This leads to a principled connection between noise resilience and the expressive capacity of parameterized quantum circuits, particularly under smart initialization strategies. Our theoretical results are supported by numerical simulations and illustrative applications.

Identifying the symmetry properties of quantum states is a central theme in quantum information theory and quantum many-body physics. In this work, we investigate quantum learning problems in which the goal is to identify a hidden symmetry of an unknown quantum state. Building on the recent formulation of the state hidden subgroup problem (StateHSP), we focus on abelian groups and develop an efficient quantum algorithm that learns any hidden symmetry subgroup using a generalized form of Fourier sampling. We showcase the versatility of the approach in three concrete applications: These are learning (i) qubit and qudit stabilizer groups, (ii) cuts along which a state is unentangled, and (iii) hidden translation symmetries. Through these applications, we reveal that well-known quantum learning primitives, such as Bell sampling and Bell difference sampling, are, in fact, special cases of Fourier sampling. Our results highlight the broad potential of the StateHSP framework for symmetry-based quantum learning tasks and provide protocols that are easier to implement on near-term quantum devices.

Abstract Preparing arbitrary quantum states requires exponential resources. Matrix product states (MPS) admit more efficient constructions, particularly when accuracy is traded for circuit complexity. Existing approaches to MPS preparation mostly rely on heuristic circuits that are deterministic but quickly saturate in accuracy, or on variational optimization methods that reach high fidelities but scale poorly. This work introduces an end-to-end MPS preparation framework that combines the strengths of both strategies within a single pipeline. Heuristic staircase-like and brick wall disentangler circuits provide warm-start initializations for variational optimization, enabling high-fidelity state preparation for large systems. Target MPSs are either specified as physical quantum states or constructed from classical datasets via amplitude encoding, using step-by-step singular value decompositions or tensor cross interpolation. The framework incorporates entanglement-based qubit reordering, reformulated as a quadratic assignment problem, and low-level optimizations that reduce depths by up to 50 % and CNOT counts by 33 % . We evaluate the full pipeline on datasets of varying complexity across systems of 19–50 qubits and identify trade-offs between fidelity, gate count, and circuit depth. Optimized brick wall circuits typically achieve the lowest depths, while the optimized staircase-like circuits minimize gate counts. Overall, our results provide principled and scalable protocols for preparing MPSs as quantum circuits, supporting utility-scale applications on near-term quantum devices.

Abstract Designing expressive yet hardware-efficient quantum circuits remains a central challenge in quantum machine learning (QML). Existing approaches to quantum circuit synthesis primarily optimize for classical performance metrics, often overlooking intrinsic quantum characteristics that govern circuit quality and generalization. This work introduces a quantumness-aware genetic optimization (QAGO) framework for circuit synthesis that integrates quantum properties such as entanglement and non-Clifford gate utilization into the evolutionary design process. We formulate circuit synthesis as both a single-objective optimization (SOO) and a multi-objective optimization (MOO) problem within a genetic framework. The SOO formulation explores quantumness-aware objectives balancing predictive performance and circuit-level quantum structure, while the MOO formulation approximates Pareto-efficient trade-offs between these goals. This dual perspective enables systematic analysis of how increasing quantum expressivity influences predictive behavior and resource cost. Experimental evaluations across three quantum kernel-based algorithms include quantum support vector machines, quantum kernel trainers, and projected quantum kernels demonstrate that circuits evolved under quantumness-aware objectives consistently outperform baseline kernel circuits such as ZZFeatureMap. Comprehensive benchmarking against classical baselines shows that QAGO achieves up to 2.5% area under the ROC curve improvement on the Higgs Boson dataset and 1.5%–9.2% gains across six of nine targets in the LIT-PCBA drug discovery benchmark. Compared to prior work (Wu et al 2021 J. Phys. G: Nucl. Part. Phys. 48 125003, Mensa et al 2023 Mach. Learn.: Sci. Technol. 4 015023) QAGO yields up to 4% improvement on Higgs and 5%–20% gains across eight of nine targets. These results provide quantitative evidence that optimizing for quantumness enhances both performance and quantum expressivity of QML models, establishing QAGO as a principled framework for quantumness-aware circuit evolution.

Abstract Local decoders, also known as cellular-automaton decoders, offer a promising path toward real-time quantum error-correction by replacing centralized classical decoding, with inherent hardware constraints, with a natively parallel and streamlined architecture from a simple local transition rule. We propose two new types of local decoders for the quantum repetition code in one dimension. The signal-rule decoders interpret odd parities between neighboring qubits as defects, attracted to each other via the exchange of binary-signals. We prove the existence of a threshold in the code-capacity model and present numerical evidence of exponential logical error suppression under a phenomenological noise model, with data and measurement errors at each error correction cycle. Compared to previously known local decoders that suffer from sub-optimal threshold and scaling, our construction significantly narrows the gap with global decoders for practical system sizes and error rates. Implementation requirements can be further reduced by eliminating the need for local classical memories, with a new rule defined on two rows of qubits. This shearing-rule works well at relevant system sizes making it an appealing short-term solution. When combined with biased-noise qubits, such as cat qubits, these decoders enable a fully local quantum memory in one dimension.

The 2024-2025 Nobel and Turing awards recognised AI and quantum science simultaneously. Yet no deployed system has brought these streams together for the public. This paper presents QSignAI, a production-deployed platform demonstrating a bidirectional AI-quantum relationship in a real-time event participation system. We address three questions: can quantum-randomness generation via a two-source extractor be embedded in an AI-driven social platform with acceptable latency; can an AI bot make quantum phenomena perceptually legible to general audiences; and does the combined system work in practice? A conversational bot routes each participant's first message through a quantum pipeline comprising a Toeplitz two-source extractor over independent single-qubit Hadamard measurements on SV1 and DM1 simulators, plus a 2-qubit Bell state, producing a unique quantum-randomness-seeded identity signature per participant. The first two questions are answered through system architecture and qualitative deployment evidence from live events; the third through successful production deployment. The current deployment uses cloud quantum simulators; physical QPU randomness is the near-term extension. Measurable benchmarks are identified as priority future work.

Quantum computing is transitioning from experimental prototypes to commercially available turnkey systems, making architecture-agnostic performance metrics essential for cross-platform comparison. Peaked Random Circuits (PRCs) have recently been proposed as a viable path to demonstrate quantum advantage on NISQ devices: a quantum processor can reliably detect a single, peaked output state amid background noise, yet the circuits' characteristics render classical simulation infeasible. In this paper, we repurpose PRCs as a system-level fidelity benchmark. By successively running a matrix of PRCs with varying qubit counts and circuit depths, we quantify a system's ability to identify the deterministic peak despite cumulative noise, gate errors, and connectivity constraints. We apply the benchmark on IQM's superconducting and AQT's trapped-ion architectures. Our results show that PRCs provide a high-precision metric comparable to Quantum Volume while exhibiting greater sensitivity to interference effects. Consequently, PRCs enable a robust framework for assessing the computational reliability of NISQ hardware across platforms.

Processing large Pauli sums is a significant bottleneck in quantum chemistry, Pauli propagation, and Pauli-based compilation. Existing frameworks often suffer from Python interpreter overhead or utilize hash-map data structures that hinder SIMD vectorization and complicate multi-threaded merging. We present PauLIB, a header-only C++20 library designed to eliminate these bottlenecks through three key architectural choices. A bit-packed binary symplectic representation that encodes each qubit in two bits, reducing Pauli multiplication to a bitwise XOR and a population count; a sorted array layout that replaces hash maps to enable branch-predictable SIMD bulk operations; and a struct-of-arrays (SoA) memory layout that exposes contiguous word arrays for explicit SIMD vectorization. Benchmarks at 500 qubits show that single Pauli string multiplication runs at 25ns per operation-14 times faster than PauliEngine and 660 times faster than Qiskit-flat across all pair counts tested. Hamiltonian outer-product multiplication is approximately 10 times faster than PauliEngine and 45 times faster than Qiskit at all tested sizes. Greedy commutation grouping, the dominant preprocessing cost in variational algorithms, achieves up to 21,000 times speedup over PennyLane, driven by the compact bit-packed representation. The compact layout reduces the memory footprint of a one-million-term Hamiltonian at 500 qubits from 1,036MB (Qiskit) to 142MB, a 7.3 times reduction that directly enables larger problem sizes within a fixed memory budget. PauLIB is open source and provides C++ and Python interfaces.

Recent demonstrations of non-Abelian braiding of graph vertices on noisy intermediate-scale quantum (NISQ) superconducting processor, and the experimental realization of topological order in general on various quantum hardware platforms necessitate an important question: when does a native (topological) fusion readout genuinely help for topological anyonic Hamiltonians implemented on NISQ hardware? We use the Fibonacci anyons chain as a concrete model for understanding the trade-off between measurement cost and compilation cost in that setting. The comparison is made against a simple grouped-Pauli baseline, and is scored by a covariance-aware mean-squared-error (MSE) of the full energy estimator. We based our benchmark on two different important classes of quantum circuits, namely Floquet time-evolved and variational quantum eigensolver quantum circuits, with the underlying Hamiltonian consisting of both braiding and fusion interaction. Our analysis found that there is not a uniform best method across both problems: the fusion readout method performed better on Floquet-type circuits on both the MSE and covariance-aware sampling variance, while the grouped Pauli method performed better on VQE on the MSE but worse on sampling variance. We derive scaling laws, and compute shot-budget crossover points, where one method is operationally favored above the other. The relevance of this work extends beyond Fibonacci chains to two-dimensional topological models compiled on superconducting and other qubit-native platforms, and can be used as a guide in answering the question of when one should measure in the native operator basis of the target physics, or when it is better to fall back on Pauli-basis reconstruction.

In classical information theory, the Doeblin coefficient of a classical channel provides an efficiently computable upper bound on the total-variation contraction coefficient of the channel, leading to what is known as a strong data-processing inequality. Here, we investigate quantum Doeblin coefficients as a generalization of the classical concept. In particular, we define various new quantum Doeblin coefficients, one of which has several desirable properties, including concatenation and multiplicativity, in addition to being efficiently computable. We also develop various interpretations of two of the quantum Doeblin coefficients, including representations as minimal singlet fractions, exclusion values, reverse max-mutual and oveloH informations, reverse robustnesses, and hypothesis testing reverse mutual and oveloH informations. Our interpretations of quantum Doeblin coefficients as either entanglement-assisted or unassisted exclusion values are particularly appealing, indicating that they are proportional to the best possible error probabilities one could achieve in state-exclusion tasks by making use of the channel. We also outline various applications of quantum Doeblin coefficients, ranging from limitations on quantum machine learning algorithms that use parameterized quantum circuits (noise-induced barren plateaus), on error mitigation protocols, on the sample complexity of noisy quantum hypothesis testing, on the fairness of noisy quantum models, and on mixing, indistinguishability, and decoupling times of time-varying channels. All of these applications make use of the fact that quantum Doeblin coefficients appear in upper bounds on various trace-distance contraction coefficients of a quantum channel. Furthermore, in all of these applications, our analysis using quantum Doeblin coefficients provides improvements of various kinds over contributions from prior literature, both in terms of generality and being efficiently computable.

A defining feature of quantum many-body systems is the exponential scaling of the Hilbert space with the number of degrees of freedom. This exponential complexity naïvely renders a complete state characterization, for instance via the complete set of bipartite Renyi entropies for all disjoint regions, a challenging task. Recently, a compact way of storing subregions' purities by encoding them as amplitudes of a fictitious quantum wave function, known as entanglement feature, was proposed. Notably, the entanglement feature can be a simple object even for highly entangled quantum states. However the complexity and practical usage of the entanglement feature for general quantum states has not been explored. In this work, we demonstrate that the entanglement feature can be efficiently learned using only a polynomial amount of samples in the number of degrees of freedom through the so-called tensor cross interpolation (TCI) algorithm, assuming it is expressible as a finite bond dimension MPS. We benchmark this learning process on Haar and random MPS states, confirming analytic expectations. Applying the TCI algorithm to quantum eigenstates of various one dimensional quantum systems, we identify cases where eigenstates have entanglement feature learnable with TCI. We conclude with possible applications of the learned entanglement feature, such as quantifying the distance between different entanglement patterns and finding the optimal one-dimensional ordering of physical indices in a given state, highlighting the potential utility of the proposed purity interpolation method.

We report the realization of an all-optical, tabletop effective negative-mass oscillator (ENMO) scheme capable of canceling quantum noise when cascaded with an optomechanical sensor susceptible to (quantum) radiation pressure noise. Our coherent quantum noise cancellation (CQNC) scheme offers a broadband cancellation capability with a tunable, wavelength-flexible, and compact system. This is achieved through the implementation of an optical equivalent of an optomechanical interaction, facilitated by a down-conversion and a beam-splitting process [Tsang and Caves, Phys. Rev. Lett. , 1 (2010)]. The intricate nature of the system and its multiple interacting components made characterizing the interdependent parameters with conventional methods ineffective, leading to the development of an characterization scheme. The obtained parameters meet the targets for CQNC set in previous studies [Wimmer , Phys. Rev. A: At. Mol. Opt. Phys. , 053836 (2014)]. With our current realization, we project a broadband quantum noise reduction of 3.6 dB, corresponding to a 77 % reduction in quantum back-action noise at the optimal frequency of maximum reduction, indicating the readiness of the ENMO for application. We discuss the prospects for new applications in quantum information and communication using the same platform.

We introduce Quantum-Adaptive KS($\varphi$) ($K$ = kickback, $S$ = sandwich), a parameterized three-qubit gate family that structurally embeds the Toffoli (CCX) gate within two additional components: (1)a palindromic Hadamard sandwich on the first control qubit $q_0$ that conjugates $Z$-type errors to $X$-type in the CCX frame, providing simultaneous sensitivity to both error types without ancilla overhead; and (2)a controlled-phase (CP) gate whose quantum phase kickback propagates post-CCX target-state information into the control-qubit phase without measurement. The term Quantum- Adaptive refers to amplitude steering conditioned by the compile-time parameter $\varphi$ via a Quantum Neural Cellular Automaton (QNCA) majority-inspired bias rule; the gate does not self-modify at runtime. Two QA-KS($π$) gates chained on a shared control qubit $q_0$ produce outputs completely orthogonal to two sequential CCX gates on $q_0$=1 inputs (output fidelity F=0.000), while agreeing exactly on $q_0$=0 inputs (F=1.000). This subspace-dependent divergence is the direct computational signature of coherent phase retention across gate boundaries -- impossible for CCX-only circuits. On the $q_1$ = 0 subspace the gate acts deterministically (up to a relative phase), providing intrinsic error non-amplification. On the $q_1$ = 1 subspace it produces four-component entangled superpositions, making it a strictly distinct quantum-native primitive from CCX. We present the complete $8 \times 8$ unitary matrix, confirmed exact to $||U^{\dagger}U-I||_{\infty} < 10^{-15}$, and define two canonical variants: QA-KS$_{π/2}$ ($\varphi = π/2$, $S$ gate) and QA-KS$_π$ ($\varphi = π$, $Z$ gate). Qiskit depolarizing-noise simulation demonstrates near-unit fidelity at $p \leq 10^{-2}$ with an honest depth cost at higher error rates. The gate preserves the three-qubit footprint of CCX with no qubit overhead.

Variational Quantum Algorithms (VQAs) potentially offer a pathway to practical quantum advantage, but their optimization is heavily hindered by barren plateaus and numerous local minima. While classically simulable Clifford circuits can warm-start VQAs to accelerate convergence, existing heuristic-based initialization methods struggle to scale within vast combinatorial search spaces. To overcome this bottleneck, we propose CRiSP (a Clifford Reinforcement Learning agent for State Preparation), a framework that formulates discrete prefix selection as a sequential decision-making problem. CRiSP utilizes Neural-Guided Monte Carlo Tree Search, driven by a Transformer-based policy trained via self-play, to insert learned Clifford gates before fixed parameterized rotations. This enables the construction of high-quality initial states entirely through polynomial-time classical stabilizer simulation without altering the underlying circuit architecture. By integrating a curriculum learning strategy that progressively expands the search horizon, the agent efficiently scales to deep circuits. Evaluated on QAOA benchmarks of up to $22$ qubits and $1{,}370$ parameters, CRiSP outperforms state-of-the-art Clifford initialization methods by a mean of $3.17\times$ (max $45.02\times$) in average energy accuracy and $2.44\times$ (max $16.01\times$) in best-achieved energy accuracy. Assessments on VQE tasks further demonstrate the framework's robustness and generalizability.

Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently emerged as an appealing computational framework for estimating these measures. Such estimators combine classical neural networks with parametrized quantum circuits, and their deployment typically entails tedious tuning of hyperparameters controlling the sample size, network architecture, and circuit topology. This work initiates the study of formal guarantees for QNEs of measured (Rényi) relative entropies in the form of non-asymptotic error risk bounds. We further establish exponential tail bounds showing that the error is sub-Gaussian and thus sharply concentrates about the ground truth value. For an appropriate sub-class of density operator pairs on a space of dimension d with bounded Thompson metric, our theory establishes a copy complexity of O ( | &amp;#x0398; ( U ) | d / &amp;#x03F5; 2 ) for QNE with a quantum circuit parameter set &amp;#x0398; ( U ) , which has minimax optimal dependence on the accuracy &amp;#x03F5; . Additionally, if the density operator pairs are permutation invariant, we improve the dimension dependence above to O ( | &amp;#x0398; ( U ) | p o l y l o g ( d ) / &amp;#x03F5; 2 ) . Our theory aims to facilitate principled implementation of QNEs for measured relative entropies and guide hyperparameter tuning in practice.

We investigate the Floquet spectrum of a detuned, driven two-level system and show that it exhibits exact quasienergy crossings when the detuning is an integer multiple of the energy quantum of the driving field. This behavior can be explained by a hidden time-nonlocal parity, which allows the Floquet modes to be classified as even or odd. Then a generic feature is the emergence of exact crossings between quasienergies of different parity. A constructive proof of the existence of the symmetry is based on a scalar recurrence relation. Moreover, we present a general scheme for its numerical computation, which can be applied to models beyond the two-level system. Analytical results are illustrated with numerical data.

Graph states are a key resource for a number of applications in quantum information theory. Due to the inherent noise in noisy intermediate-scale quantum (NISQ) era devices, it is important to understand the effects noise has on the usefulness of graph states. We consider a noise model where the initial qubits, prepared in | + &amp;#x27E9; states, undergo depolarizing noise before the application of the CZ operations that generate edges between qubits situated at the nodes of the resulting graph state. For this model we develop a method for calculating the coherent information – a lower bound on the rate at which entanglement can be distilled, across a bipartition of the graph state. We also identify some patterns on how adding more nodes or edges affects the bipartite distillable entanglement. As an application, we find a family of graph states that maintain a strictly positive coherent information for any amount of (non-maximal) depolarizing noise.

Neutral-atom arrays provide a versatile platform for quantum information processing. However, in large-scale arrays, efficient photon collection remains a bottleneck for key tasks such as fast, nondestructive qubit readout and remote entanglement distribution. We propose a cavity-based approach that enables fast, parallel operations over many atoms using multiple modes of a single optical cavity. By selectively shifting the relevant atomic transitions, each atom can be coupled to a distinct cavity mode, allowing independent simultaneous processing. We present practical system designs that support cavity-mode multiplexing with up to 50 modes, enabling rapid mid-circuit syndrome extraction and significantly enhancing entanglement distribution rates between remote atom arrays. This approach offers a scalable solution to core challenges in neutral-atom arrays, advancing the development of practical quantum technologies.

Pulse-level simulators are the lowest-level, most widely used abstraction layer for studying how quantum hardware responds to control signals, but they can be built on Hamiltonian models with very different fidelity and cost. This raises the question: which level of physical abstraction is sufficient for a given simulation objective? We study this question for a flux-tunable two-qubit superconducting device with a fixed bus coupler by comparing three Hamiltonian descriptions of the same hardware: an effective two-level model, a three-mode Duffing model, and a circuit-based transmon model in the charge basis. Using a realistic parameter set, we evaluate these models on a common benchmark suite spanning flux-dependent spectra, extracted two-qubit interaction terms, driven single-qubit dynamics, CZ gate dynamics, leakage outside the computational subspace, and runtime. Across the tested flux range, the Duffing model follows the circuit-based reference more closely than the effective model for static spectra and reduced two-qubit quantities, while in driven benchmarks, the multilevel models reveal effects absent in the effective description. Overall, the results support a layered use of abstraction in pulse-level simulation: effective models for reduced analyses, Duffing models as a practical multilevel default, and circuit-based models for high-fidelity reference simulation or detailed leakage analysis.

Quantum computing promises to solve problems beyond the reach of classical computers, but today's quantum hardware is error-prone and much slower than classical hardware. Every quantum operation is costly, making it crucial to minimize quantum resource usage in near-term algorithms. Quantum resources should only be used when they are truly essential for quantum advantage, and not wasted on operations that can be efficiently handled by classical computation. In this work, we focus on de-quantizing quantum operations to classical computation whenever possible. The approach we propose for this is hybrid quantum-classical constant propagation, an optimization which reduces quantum operations by trading them for fast, reliable classical instructions. This is done by tracking between quantum and classical states to identify and eliminate unnecessary quantum gates and controls. We formalize a hybrid state model for quantum-classical constant propagation, implement our optimizations in the open-source MQT Core tool, and evaluate them on benchmark circuits. The obtained results show that quantum-classical constant propagation can reduce costly multi-qubit operations, making quantum programs more practical and robust for near-term devices. This opens the door to new hybrid compiler strategies that leverage the best of both quantum and classical worlds.

Negative Selection Algorithms (NSAs), inspired by the self/non-self discrimination mechanism of the human immune system, have been widely employed in anomaly detection. However, their effectiveness is often constrained by the efficiency of detector generation. This paper presents the Quantum Genetic Negative Selection Algorithm (QGNSA), a novel approach that integrates a Quantum Genetic Algorithm (QGA) into the EvoSeedRNSA algorithm, replacing its classical evolutionary optimization process. The proposed method exploits quantum superposition and probabilistic amplitude adjustment to enhance search space exploration and convergence efficiency in the detector generation process. Empirical evaluations using the Metaverse Financial Transactions Dataset demonstrate that QGNSA achieves superior anomaly detection accuracy compared to its classical counterpart while maintaining robustness under varying hyperparameter configurations. The experimental results highlight the potential advantages of quantum computing in artificial immune systems, particularly in high-dimensional anomaly detection tasks. Future research will focus on further optimizing quantum circuit design, deploying the algorithm on real quantum hardware, and exploring hybrid quantum-classical approaches for improved computational efficiency.

Minimising EPR consumption is the dominant objective when routing a quantum circuit on a distributed quantum computer (DQC). We present dSABRE, a SABRE-style router for multi-core processors that, on each iteration of a lookahead-driven loop, first resolves any intra-core front-layer gates by SWAP scoring and only falls back to scoring inter-core teleportation candidates when the intra-core front is empty. Three mechanisms drive the improvement over the state of the art: a five-term gate-centric teleportation score that generalises the local SWAP heuristic to the inter-core setting, whose explicit capacity-penalty term keeps the scorer from teleporting into saturated cores; a proactive congestion-relief pass that redistributes idle qubits out of high-demand cores before deadlock; and a BFS-layer construction of the inter-core extended set that respects DAG dependencies layer by layer rather than mixing wires in topological order. Across 18 MQT-Bench circuits at 25, 36, and 64 logical qubits, dSABRE reduces geometric-mean EPR consumption by 41-44% over TeleSABRE and by 16-68% over the gate-teleportation-based pytket-dqc, using standard Qiskit SabreLayout for the initial layout. A large-circuit QFT sweep at 100-360 qubits confirms scalability. Code and online appendices are available at https://github.com/ebony72/dsabre.

Quantum computing involving physical systems with continuous degrees of freedom, such as the quantum states of light, has recently attracted significant interest. However, a well-defined quantum complexity theory for these bosonic computations over infinite-dimensional Hilbert spaces is missing. In this work, we lay foundations for such a research program. We introduce natural complexity classes and problems based on bosonic generalizations of BQP, the local Hamiltonian problem, and QMA. We uncover several relationships and subtle differences between standard Boolean classical and discrete variable quantum complexity classes and identify outstanding open problems. In particular: 1. We show that the power of quadratic (Gaussian) quantum dynamics is equivalent to the class BQL. More generally, we define classes of continuous-variable quantum polynomial time computations with a bounded probability of error based on higher-degree gates. Due to the infinite dimensional Hilbert space, it is not a priori clear whether a decidable upper bound can be obtained for these classes. We identify complete problems for these classes and demonstrate a BQP lower and EXPSPACE upper bound. We further show that the problem of computing expectation values of polynomial bosonic observables is in PSPACE. 2. We prove that the problem of deciding the boundedness of the spectrum of a bosonic Hamiltonian is co-NP-hard. Furthermore, we show that the problem of finding the minimum energy of a bosonic Hamiltonian critically depends on the non-Gaussian stellar rank of the family of energy-constrained states one optimizes over: for constant stellar rank, it is NP-complete; for polynomially-bounded rank, it is in QMA; for unbounded rank, it is undecidable.

We time-evolve a translationally invariant quantum state on the Quantinuum H1-1 trapped-ion quantum processor, studying the dynamical quantum phase transition of the transverse field Ising model. This physics requires a delicate cancellation of phases in the many-body wavefunction and presents a tough challenge for current quantum devices. We follow the dynamics using a quantum circuit matrix product state ansatz, optimised for the time-evolution using a fidelity cost function. Sampling costs are mitigated by using the measured values of this circuit as stochastic corrections to a simple classical extrapolation of the ansatz parameters. Our results demonstrate the feasibility of variational quantum time-evolution and reveal a hitherto hidden simplicity of the evolution of the transverse-field Ising model through the dynamical quantum phase transition.

There is great interest in generating and controlling entanglement in Bose-Einstein condensates and similar ensembles for use in quantum computation, simulation, and sensing. One class of entangled states useful for enhanced metrology are spin-squeezed states of N two-level atoms. After preparing a spin coherent state of width 1 / N centered at coordinates ( &amp;#x03B8; , &amp;#x03D5; ) on the Bloch sphere, atomic interactions generate a nonlinear evolution that shears the state's probability density, stretching it to an ellipse and causing squeezing in a direction perpendicular to the major axis. Here we consider the same setup but in the N &amp;#x2192; &amp;#x221E; limit . This shrinks the initial coherent state to zero area. Large N also suppresses two-particle entanglement and squeezing, as required by a monogamy bound. The torsion (1-axis twist) is still present, however, and the center of the large N coherent state evolves as a qubit governed by a two-state Gross-Pitaevskii equation. The resulting nonlinearity is known to be a powerful resource in quantum computation. It can be used to implement single-input quantum state discrimination, an impossibility within linear one-particle quantum mechanics. We obtain a solution to the discrimination problem in terms of a Viviani curve on the Bloch sphere. We also consider an open-system variant containing both Bloch sphere torsion and dissipation. In this case it should be possible to generate two basins of attraction within the Bloch ball, having a shared boundary that can be used for a type of autonomous state discrimination. We explore these and other connections between spin squeezing in the large N limit and nonlinear quantum gates, and argue that a two-component condensate is a promising platform for realizing a nonlinear qubit.

Abstract The non-equilibrium thermodynamics of interacting quantum many-body systems is investigated within the framework of thermal time-dependent density functional theory (DFT) using a generalized linear-response formulation for the full quantum work statistics. A first-principles route is established to reconstruct the relaxation function that underlies linear-response theory, thereby moving beyond phenomenological descriptions and enabling a consistent evaluation of all moments of the dissipated-work distribution in interacting systems. The predictive power of the approach is demonstrated for the Hubbard model subject to a staggered external potential, where the evolution of the relaxation dynamics during the Mott-to-band-insulator crossover reveals how distinct many-body phases shape the out-of-equilibrium thermodynamic response. These results provide a microscopic and transferable framework for quantum thermodynamics in correlated systems, bridging thermal DFT and non-equilibrium work statistics.

Abstract The coherence of superconducting quantum computers is severely limited by material defects that create parasitic two-level-systems (TLS). Progress is complicated by lacking understanding how TLS are created and in which parts of a qubit circuit they are most detrimental. Here, we present a method to determine the individual positions of TLS at the surface of a transmon qubit. We employ a set of on-chip gate electrodes near the qubit to generate local DC electric fields that are used to tune the TLS’ resonance frequencies. The TLS position is inferred from the strengths at which TLS couple to different electrodes and comparing them to electric field simulations. We found that the majority of detectable surface-TLS was residing on the leads of the qubit’s Josephson junction, despite the dominant contribution of its coplanar capacitor to electric field energy and surface area. This indicates that the TLS density is significantly enhanced near shadow-evaporated electrodes fabricated by lift-off techniques. Our method is useful to identify critical circuit regions where TLS contribute most to decoherence, and can guide improvements in qubit design and fabrication methods.

Abstract We show that the quantum advantages arising from incompatibility of a set of measurements cannot be enhanced by subjecting them to a filter, namely, by combining them with a device that post-selects the incoming states on a fixed outcome of a stochastic transformation. This result holds for several measures of incompatibility, such as those based on robustness and convex weight. As an application, we show that, for Einstein-Podolsky-Rosen steering, our no-go results determine the maximum steerability attainable under the most general local filters, together with an explicit expression for the optimal filter. Moreover, our results generalize to nonphysical maps, i.e., positive but not completely positive linear maps.

Floquet quantum circuits are able to realise a wide range of non-equilibrium quantum states, exhibiting quantum chaos, topological order and localisation. In this work, we investigate the stability of operator localisation and emergence of chaos in random Floquet-Clifford circuits subjected to unitary perturbations which drive them away from the Clifford limit. We construct a nearest-neighbour Clifford circuit with a brickwork pattern and study the effect of including disordered non-Clifford gates. The perturbations are uniformly sampled from single-qubit unitaries with probability p on each qubit. We show that the interacting model exhibits strong localisation of operators for 0 &amp;#x2264; p &amp;#x003C; 1 that is characterised by the fragmentation of operator space into disjoint sectors due to the appearance of wall configurations. Such walls give rise to emergent local integrals of motion for the circuit that we construct exactly. We analytically establish the stability of localisation against generic perturbations and calculate the average length of operator spreading tunable by p . Although our circuit is not separable across any bi-partition, we further show that the operator localisation leads to an entanglement bottleneck, where initially unentangled states remain weakly entangled across typical fragment boundaries. Finally, we study the spectral form factor (SFF) to characterise the chaotic properties of the operator fragments and spectral fluctuations as a probe of non-ergodicity. In the p = 1 model, the emergence of a fragmentation time scale is found before random matrix theory sets in after which the SFF can be approximated by that of the circular unitary ensemble. Our work provides an explicit description of quantum phases in operator dynamics and circuit ergodicity which can be realised on current NISQ devices.

Physical computing systems provide a promising route toward hardware-native machine learning, but their computational capabilities remain difficult to characterize in a principled, task-independent, and data-efficient way. We extend the Information Processing Capacity (IPC) framework to stationary physical computing systems and establish several fundamental results: individual capacities are bounded between zero and one, their sum over a complete basis is bounded by the number of readouts, and noise strictly reduces this bound. We address the finite-sample estimation of IPC and derive the asymptotic form of the systematic positive bias affecting naive estimators. Building on these results, we introduce data-efficient estimation methods based on Richardson extrapolation and Sobol quasi-random sampling. We validate the framework experimentally using a photonic computing system based on picosecond laser pulses propagating through a nonlinear optical fibre. By varying the laser power and fibre length, we observe systematic shifts of the IPC distribution toward higher-order nonlinear capacities induced by the Kerr effect. Finally, we demonstrate that the total IPC strongly correlates with performance on benchmark machine-learning tasks and provides a reliable estimate of the effective dimensionality of the system. These results establish IPC as a practical bridge between the intrinsic dynamics of physical computing systems and their machine-learning performance.

Multi-controlled Toffoli gates are fundamental building blocks in quantum computation, with applications in quantum arithmetic, simulation, and search algorithms. In fault-tolerant architectures, their realization is constrained by the high cost of non-Clifford resources, particularly in terms of T-count and T-depth. Recent advances have demonstrated that the use of ancillary qubits, relative-phase Toffoli gates, and dynamic circuit techniques can substantially reduce this overhead. In this work, we investigate the decomposition of large Toffoli gates using 3- and 4-input relative-phase Toffoli gates in the presence of a single clean ancilla and conditionally clean ancillas. We derive explicit resource bounds for Clifford+T implementations incorporating dynamic-circuit-based uncomputation and measurement-conditioned corrections. Our analysis emphasizes T-depth reduction under fixed CX and T-count overhead, ensuring relevance for near-term devices. We show that introducing 4-input relative-phase Toffoli gates enables significant T-depth reductions through enhanced parallelism while maintaining favorable ancilla requirements. We further validate our theoretical results through experimental evaluation and comparative analysis with existing approaches.

The Toffoli gate is a fundamental building block for quantum arithmetic and reversible logic, yet its efficient realization remains a major challenge in both near-term and fault-tolerant quantum architectures. Recent advances in dynamic quantum circuit capabilities, including mid-circuit measurement and classical feedforward, provide new opportunities for reducing the resource overhead of non-Clifford operations. In this work, we propose a set of dynamic decomposition strategies for multi-controlled Toffoli gates that exploit adaptive circuit execution and ancilla-assisted constructions. Our methods systematically reduce entangling-gate count, T-count, and T-depth compared with conventional static decompositions, while preserving fault-tolerance guarantees. Through analytical cost models and experimental evaluation, we demonstrate that relative-phase primitives and measurement-conditioned corrections enable scalable implementations with improved depth and resource efficiency.

Abstract We propose an inverse-squeezing Kennedy receiver for discriminating binary phase-shift-keyed displaced squeezed vacuum states. The receiver combines a Kennedy-type nulling displacement, an orthogonally oriented inverse-squeezing operation and photon-number-resolving detection with a maximum-a- posteriori threshold rule. Its key mechanism is that the inverse-squeezing stage converts transmitter-side squeezing into enhanced photon-number contrast, or equivalently an effective coherent-state energy gain, that can be directly exploited at the measurement stage. Under ideal equal-prior conditions, the receiver surpasses the standard quantum limit for squeezed-state binary phase-shift keying at approximately N ≈ 0.3, outperforms the Helstrom bound of coherent-state binary phase-shift keying at approximately N ≈ 0.4, and reaches the 1% error level near N ≈ 0.6. We further analyze its performance under realistic imperfections, including finite detector efficiency, dark counts, channel phase diffusion, receiver thermal noise and transmission loss. The results show that adaptive thresholding preserves robust performance against detector and noise imperfections over practical parameter ranges, whereas transmission loss progressively suppresses the squeezing-enabled advantage. These findings indicate that, for the fixed source parametrization adopted in this work, the proposed receiver is most advantageous in the low-loss regime, especially at low source energies.

Abstract Bosonic quantum systems operate in an infinite-dimensional Hilbert space, unlike discrete-variable quantum systems. This distinct mathematical structure leads to fundamental differences in quantum information processing, such as exponentially greater complexity of state tomography 1 and factoring in constant space 2 . Yet, it remains unclear whether this structural difference may translate to a practical computational advantage over finite-dimensional quantum computers. Here we take a step towards answering this question by showing that universal bosonic quantum computations can be simulated in polynomial space (and exponential time) on a classical computer, improving the previous best upper bound requiring exponential memory 3 . In complexity-theoretic terms, we improve the best upper bound on CVBQP with at most exponential energy from EXPSPACE to PSPACE. This result is achieved using a simulation strategy based on finite energy cutoffs and approximate coherent state decompositions. While we propose ways to potentially refine this bound, we also present arguments supporting the plausibility of an exponential computational advantage of bosonic quantum computers over their discrete-variable counterparts. Furthermore, we emphasize the role of circuit energy as a resource and discuss why it may act as the fundamental bottleneck in realizing this advantage in practice.

Abstract Motivated by recent advances in the single-step implementation of n -control-qubit Toffoli gates, we propose a broad class of generalized Toffoli gates with multiple control qubits that can be executed in a single step using a feasible and unified framework based on Ising-type interactions. Unlike the standard Toffoli gate condition, which flips the target qubit only when all control qubits are in the $$|1\rangle$$ | 1 〉 state, our generalized gates allow for diverse, customizable control conditions, including: mixed control, Hamming weight control, weighted Hamming control, multiple-designated configurations, threshold control, multiple-target control, and multiple-option control. Simulation results demonstrate that these gates offer substantial advantages in both feasibility and reliability over decompositions into standard 2-control-qubit Toffoli gates and other primitive gates, significantly reducing circuit depth, execution time, and error rates.

The accelerating convergence of smart metering, generative artificial intelligence, and quantum-inspired combinatorial optimisation is reshaping how energy utilities manage physical infrastructure, customer engagement, and environmental accountability

The Boolean Satisfiability (SAT) problem is a canonical NP-complete problem and a natural candidate for quantum acceleration via search-based algorithms. In Grover-based quantum SAT solvers, the dominant computational cost stems from the construction of a reversible oracle that evaluates the Boolean formula, rendering the choice of SAT encoding crucial for overall quantum resource efficiency. Although SAT instances are conventionally expressed in Conjunctive Normal Form (CNF), such encodings typically translate into quantum circuits with significant qubit overhead and high non-Clifford gate complexity. In this work, we investigate an Exclusive-Sum-of-Products (ESOP)-based CNF (e-CNF) representation tailored for quantum SAT solving and analyze its impact on oracle construction. We derive tighter upper bounds on qubit requirements and Clifford+$T$ gate counts for Grover-based SAT solvers when e-CNF encodings are employed in place of standard CNF. In addition, we propose a scalable transformation from Boolean formulas to e-CNF and present a systematic procedure for interpreting e-CNF representations as reversible quantum circuits suitable for oracle implementation. Experimental evaluation on representative SAT benchmarks demonstrates that the proposed e-CNF-based approach yields substantial and consistent reductions in quantum resources, including qubit count, T-gate complexity, and circuit depth, when compared to CNF-based oracle constructions. These results establish e-CNF as an effective quantum-aware SAT encoding that significantly improves the practicality of oracle-based quantum SAT solving.

Order finding is the core subroutine of Shor's algorithm. On NISQ hardware, phase estimation output distributions are often distorted by noise, making correct order recovery difficult. We study recoverability in noisy order finding: given a measured precision-register distribution, when does standard classical post-processing still return the true order? We analyze 680 distributions from IBM quantum systems across problem instances and circuit settings. For each distribution, we apply continued-fraction post-processing with modular verification and define recoverability as whether the recovered order equals the true one. We characterize each distribution using four features: autocorrelation peak strength, normalized entropy, dominant verified mass fraction, and verified margin fraction. We evaluate these quantities using marginal feature comparisons, single-feature AUROC analysis, and multivariate tree-based classifiers. We use random-forest permutation importance to assess which quantities contribute distinct predictive information once the other features are known. To make classification behavior interpretable, we train a decision tree that exposes threshold rules for recoverable and non-recoverable distributions. We find that recoverability is strongly associated with residual comb-like structure in the measured distribution and the way verified probability mass is organized across candidate denominators. The dominant verified mass fraction is the strongest single-feature indicator of recoverability, and tree-based analysis shows it also provides the primary split in an interpretable threshold description. Some highly distorted distributions remain recoverable when one verified denominator dominates the post-processing mass, while some visibly structured distributions fail because classical post-processing favors an incorrect verified denominator.

We study mutually unbiased bases (MUBs) as structured finite initialization and adaptation families for variational quantum algorithms. The main theoretical result is that, in every dimension admitting a complete set of MUBs, the complete MUB ensemble maximizes isotropic Gaussian random-Hamiltonian width among all unions of d+1 orthonormal bases in C^d. Equivalently, within this basis-union class, it gives the smallest expected best-of-set minimum for random-Hamiltonian minimization. The proof represents each orthonormal basis as a regular-simplex Gaussian block and uses a centered-convex Gaussian correlation inequality to show that the independent-block case, realized by complete MUBs, is stochastically extremal. We also record a radial extension for Hamiltonians H=RG with R nonnegative and independent, and the unrestricted qubit case, where complete qubit MUBs are globally optimal among arbitrary six-state ensembles by a Bloch-sphere/octahedron mean-width argument. We then separate this coverage theorem from variational training dynamics. For diagonal QUBO costs, the MUB-family dependence of a fully matched construction collapses; for the canonical b=0 label it reduces to ordinary X-mixer QAOA. The empirical method is therefore adaptive MUB-XRot warm-start QAOA rather than canonical matched-mixer MUB-QAOA. In a cross-problem benchmark over MaxCut, weighted MaxCut, MIS, weighted MIS, and knapsack, adaptive MUB-XRot is non-worse than standard QAOA in 80.0% of 1500 paired cases, with win/tie/loss 829/371/300 and mean decoded-ratio improvement +0.1616. A separate QRAO MaxCut study shows that bit-flip MUB-family search reaches mean relaxed ratio 0.921 and improves over the X-variational baseline by +0.0608. The evidence is quality-oriented and incurs substantial runtime overhead; no quantum-advantage claim is made.

Advances in quantum computing challenge the hardness assumptions underlying widely deployed public-key cryptography in blockchain systems. Although post-quantum cryptography (PQC) standards are emerging, understanding quantum risk remains fragmented across research, engineering, governance, and investment communities. This demo presents Quantum Futures Interactive, a live interdisciplinary demonstration combining educational visualization, participatory interaction, and demonstrative post-quantum artifact generation using a toy LWE-based construction. Participants engage in a structured seven-stage interaction flow covering quantum threat education, sentiment capture, technology prioritization, infrastructure tradeoff exploration across simulators and QPUs, and artifact generation. The system integrates distributed trust concepts and sustainability-aware infrastructure considerations within an interactive decision framework.

Abstract Continuous-variable quantum secret sharing (CVQSS) is a promising approach to ensuring multi-party information security. While CVQSS offers practical ease of implementation, its present performance remains limited. In this paper, we propose a novel CVQSS protocol integrated with a state-discrimination detector (SDD), dubbed SDD-CVQSS. In particular, we first develop the detailed procedure of SDD-CVQSS, which replaces the traditional coherent detector with an SDD and eliminates the long-standing necessary step of establishing multiple point-to-point quantum key distribution links between all users and the dealer. We then elaborate on the principle of the specifically designed SDD, which can efficiently discriminate interfered states with a much lower error probability. Finally, we construct a security model for SDD-CVQSS and derive its security bound against both eavesdroppers and dishonest users. Numerical simulations show that SDD-CVQSS outperforms conventional CVQSS in terms of both maximum transmission distance and secret key rate, and its performance is even superior to the PLOB bound. Additionally, we find that the performance degradation of SDD-CVQSS in long-distance transmission scenarios can be effectively compensated for using a post-selection scheme, providing a feasible way to achieve high-performance CVQSS.

Abstract Fusion-based quantum computing is an attractive model for fault-tolerant computation based on photonics requiring only finite-sized entangled resource states followed by linear-optics operations and photon measurements. Large-scale implementations have so far been limited due to the access only to probabilistic photon sources, vulnerability to photon loss, and the need for massive multiplexing. Deterministic photon sources offer an alternative and resource-efficient route. By synergistically integrating deterministic photon emission, adaptive repeat-until-success fusions, and an optimised architectural design, we propose a complete blueprint for a photonic quantum computer using quantum dots and linear optics. It features time-bin qubit encoding, reconfigurable entangled-photon sources, and a fusion-based architecture with low optical connectivity, significantly reducing the required optical depth per photon and resource overheads. We present in detail the hardware required for resource-state generation and fusion networking, experimental pulse sequences, and exact resource estimates for preparing a logical qubit. We estimate that one logical clock cycle of error correction can be executed within microseconds, which scales linearly with the code distance. We also simulate error thresholds for fault-tolerance considering a full catalogue of intrinsic error sources found in real-world quantum dot devices. Our work establishes a practical blueprint for a low-optical-depth, emitter-based fault-tolerant photonic quantum computer.

Abstract Combining quantum sensing with quantum computing can lead to quantum computational sensing (QCS) protocols that are able to more efficiently extract task-specific information from physical signals than is possible otherwise. In this paper, we present, in theory and numerical simulations, the application of two quantum algorithms—quantum signal processing and quantum neural networks—to various binary and multiclass machine-learning classification tasks in sensing. Here, sensing operations are interleaved with computing operations, giving rise to nonlinear functions of the sensed signals. Our approach to optimizing QCS protocols takes into account quantum sampling noise and allows us to engineer protocols that can yield accurate results with as few as just a single measurement shot. In all cases, we have been able to show a regime of operation where a quantum computational sensor can achieve higher accuracy than a conventional quantum sensor for a given budget of sensing time, with a simulated accuracy advantage of &gt;20 percentage points for some tasks. We also present protocols for performing nonlinear tasks using Hamiltonian-engineered bosonic systems and quantum signal processing with hybrid qubit-bosonic systems, and empirically show an advantage when the received signal has a limited mean photon number.

Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of efficient general-state encoding circuits an important problem, particularly with respect to two-qubit gate count and circuit depth. Yet the synthesis of such encoders has been studied less extensively than general Clifford circuit synthesis or the preparation of specific logical Pauli-eigenstates. In this work, we develop methods for synthesizing efficient encoders for arbitrary stabilizer codes. We formulate encoder synthesis as a search over stabilizer tableaus and introduce greedy and rollout-based algorithms that exploit the freedom among stabilizer-equivalent realizations of the same encoding isometry. For code families with a modular structure, such as generalized concatenated and holographic codes, we show how large encoders can be assembled from optimized local constituent encoders, and we use SMT-based exact synthesis to obtain optimal local circuits for small instances. We further evaluate the proposed methods on a broad set of stabilizer codes, including holographic and quantum low-density parity-check (qLDPC) codes, and compare them against recent encoder-synthesis methods and existing constructions from the literature, obtaining improvements of up to 43% in two-qubit gate count and up to 70% in depth. Our results support the optimization of encoded-state preparation in several fault-tolerant quantum-computing schemes, and all methods are openly available as part of the Munich Quantum Toolkit.

The conversation in finance has officially shifted from "when will quantum arrive?" to "how is quantum performing in production?" At IonQ, we are now demonstrating that production-level portfolio optimization is solvable today.

Quantum paradoxes show that the outcomes of different quantum measurements cannot be described by a single measurement-independent reality. Any theoretical description of a quantum measurement implies the selection of a specific measurement context. Here, we investigate generalised quantum measurements, in order to identify the mechanism by which this specific context is selected. We show that external quantum fluctuations, represented by the initial state of the measurement apparatus, play an essential role in the selection of the context. This has the non-trivial consequence that, when considering measurements other than just idealised projection-valued measures, different outcomes of a single measurement setup can represent different measurement contexts. We further show this result underpins recent claims that contextuality can occur in scenarios without measurement incompatibility.

This work considers a teleportation task for Alice and Bob in a scenario where Bob cannot perform corrections. In particular, we analyse the task of multicopy state teleportation , where Alice has k identical copies of an arbitrary unknown d -dimensional qudit state | &amp;#x03C8; &amp;#x27E9; to teleport a single copy of | &amp;#x03C8; &amp;#x27E9; to Bob using a maximally entangled two-qudit state shared between Alice and Bob without Bob's correction. Alice may perform a joint measurement on her half of the entangled state and the k copies of | &amp;#x03C8; &amp;#x27E9; . We prove that the maximal probability of success for teleporting the exact state | &amp;#x03C8; &amp;#x27E9; to Bob is p ( d , k ) = k d ( k &amp;#x2212; 1 + d ) and present an explicit protocol to attain this performance. Then, by utilising k copies of an arbitrary target state | &amp;#x03C8; &amp;#x27E9; , we show how the multicopy state teleportation protocol can be employed to enhance the success probability of storage and retrieval of quantum programs, which aims to universally retrieve the action of an arbitrary quantum channel that is stored in a state. Our proofs make use of group representation theory methods, which may find applications beyond the problems addressed in this work.

A class of quantum resource theories, based on non-convex star-shape sets, presented in this work captures the key quantum properties that cannot be studied by standard convex theories. We provide operational interpretations for a resource of this class and demonstrate its advantage to improve performance of correlated quantum discrimination tasks and testing of quantum combs. Proposed techniques provide useful tools to describe quantum discord, total correlations in composite quantum systems and to estimate the degree of non-Markovianity of an analyzed quantum dynamics. Other applications include the problem of unistochasticity of a given bistochastic matrix, with relevance for quantization of classical dynamics and studies of violation of CP-symmetry in high energy physics. In all these cases, the non-linear witnesses introduced here outperform the standard linear witnesses. Importance of our findings for quantum information theory is also emphasized.

Abstract It is univocally anticipated that in a theory of quantum gravity, there exist quantum superpositions of semiclassical states of spacetime geometry. Such states could arise, for example, from a source mass in a superposition of spatial configurations. In this paper, we introduce a framework for describing such “quantum superpositions of spacetime states.” We introduce the notion of the relativity of spacetime superpositions, demonstrating that for states in which the superposed amplitudes differ by a coordinate transformation, it is always possible to re-express the scenario in terms of dynamics on a single, fixed background. Our result unveils an inherent ambiguity in labelling such superpositions as genuinely quantum-gravitational, which has been done extensively in the literature, most notably with reference to recent proposals to test gravitationally-induced entanglement. We apply our framework to the above-mentioned scenarios, looking at gravitationally-induced entanglement, the problem of decoherence of gravitational sources, and clarifying commonly overlooked assumptions. In the context of decoherence of gravitational sources, our result implies that the resulting decoherence is not fundamental, but depends on the existence of external systems that define a relative set of coordinates through which the notion of spatial superposition obtains physical meaning.

Public access to pulse-level and control-electronics interfaces in commercial quantum computing has bifurcated. This paper proposes a six-axis rubric for measuring control-plane openness, the layer between gate-level circuit specification and physical control electronics, defined operationally so that the same evidence produces the same grade across vendors. The rubric is validated three ways: a blinded re-grading pass that tests whether the cited evidence and the level definitions alone reproduce the recorded grades, a boundary-case methodology that fixes where each level begins and ends, and a published grading protocol that lets others reproduce and contest any cell. A time-point comparison anchored on the February 2025 removal of pulse-level access from IBM hardware establishes that the rubric measures change rather than describing a snapshot. The rubric is applied to thirteen commercial vendors across superconducting, trapped-ion, neutral-atom, and photonic modalities as of May 1, 2026, and one of the three harms it detects is demonstrated through a reproduction-access audit of five pre-2025 IBM Qiskit Pulse experiments, carried through to a structural port to Rigetti Quil-T. The catalog ships as a machine-readable artifact under CC-BY-4.0 with per-cell source URLs (https://doi.org/10.5281/zenodo.20163276). The readings will go stale; the rubric is the contribution that survives them.

Fermionic quantum processors are a promising platform for quantum simulation of correlated fermionic matter. In this work, we study a hardware-efficient protocol for measuring complex expectation values of the time-evolution operator, commonly referred to as Loschmidt echoes, with fermions in an optical superlattice. We analyze the algorithm for the Fermi–Hubbard model at half-filling as well as at finite doping. The method relies on global quench dynamics and short imaginary time evolution, the latter being realized by architecture-tailored pulse sequences starting from a product state of plaquettes. Our numerical results show that complex Loschmidt echoes can be efficiently obtained for large many-body states over a broad spectral range. This allows one to measure spectral properties of the Fermi–Hubbard model, such as the local density of states, and paves the way for the study of finite-temperature properties in current fermionic quantum simulators.

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) have provided a unified framework for understanding many quantum algorithms, including factorization, matrix inversion, and Hamiltonian simulation. As a multivariable version of QSP, multivariable quantum signal processing (M-QSP) is proposed. M-QSP interleaves signal operators corresponding to each variable with signal processing operators, which provides an efficient means to perform multivariable polynomial transformations. However, the necessary and sufficient condition for what types of polynomials can be constructed by M-QSP is unknown. In this paper, we propose a classical algorithm to determine whether a given pair of multivariable Laurent polynomials can be implemented by M-QSP, which returns True or False. As one of the most important properties of this algorithm, its returning True is the necessary and sufficient condition. The proposed classical algorithm runs in polynomial time in the number of variables and signal operators. Our algorithm also provides a constructive method to select the necessary parameters for implementing M-QSP. These findings offer valuable insights for identifying practical applications of M-QSP.

Quantum low-density parity-check codes are a promising approach to fault-tolerant quantum computation, offering potential advantages in rate and decoding efficiency. In this work, we introduce quantum Margulis codes, a new class of QLDPC codes derived from Margulis&amp;apos; classical LDPC construction via the two-block group algebra framework. We show that quantum Margulis codes, unlike bivariate bicycle codes which require ordered statistics decoding for effective error correction, can be efficiently decoded using a standard min-sum decoder with linear complexity, when decoded under the code capacity noise model. This is attributed to their Tanner graph structure, which does not exhibit group symmetry, thereby mitigating the well-known problem of error degeneracy in QLDPC decoding. To further enhance performance, we propose an algorithm for constructing 2BGA codes with controlled girth, ensuring a minimum girth of 6 or 8, and use it to generate several quantum Margulis codes of length 240 and 642. We validate our approach through numerical simulations, demonstrating that quantum Margulis codes behave significantly better than BB codes in the error floor region, under min-sum decoding.

Classical machine learning has proven remarkably useful in post-processing quantum data, yet typical learning algorithms often require prior training to be effective. In this work, we employ a tensorial kernel support vector machine (TK-SVM) to analyze experimental data produced by trapped-ion quantum computers. This unsupervised method benefits from directly interpretable training parameters, allowing it to identify the non-trivial string-order characterizing symmetry-protected topological (SPT) phases. We apply our technique to two examples: a spin-1/2 model and a spin-1 model, featuring the cluster state and the AKLT state as paradigmatic instances of SPT order, respectively. Using matrix product states, we generate a family of quantum circuits that host a trivial phase and an SPT phase, with a sharp phase transition between them. For the spin-1 case, we implement these circuits on two distinct trapped-ion machines based on qubits and qutrits. Our results demonstrate that the TK-SVM method successfully distinguishes the two phases across all noisy experimental datasets, highlighting its robustness and effectiveness in quantum data interpretation.

In superconducting devices running variational workloads, gate and readout fidelities drift on hour timescales, while existing runtime schedulers treat backend quality as static. The temporal dimension of calibration remains unresolved. We formulate runtime calibration as a state-trajectory feedback-control problem under a fixed wall-clock budget, and investigate whether spending time on calibration now can improve the future optimization trajectory. Calibration quality proxy is represented as a drifting equivalent-age state, recovery action is modeled as costly state reset, and policies are evaluated by time-integrated optimization gap over the full execution window. Using a finite-horizon rollout controller, we compare feedback calibration against a strengthened family of open-loop baselines across three latency regimes: cloud-like (25 ms), local-millisecond (1 ms), and tight-loop (4 $\mathrmμ$s). The results show a clear ordering: cloud-like feedback is generally uncompetitive, while local-ms and tight-loop regimes open a positive-gain region that grows with workload quality-sensitivity and initial calibration age. Crucially, the gap between local-ms and tight-loop control is modest for single-target recovery. The advantage of tight-loop integration emerges under capacity pressure, when many calibration targets must be processed within the same control window.

Quantum processors are being integrated into HPC ecosystems as co-processors, where compilation of quantum circuits into hardware-executable form determines both output fidelity and runtime. Current compilers use a fixed pass sequence and ignore the fact that optimal pass selection varies with circuit, hardware, and noise conditions. We present TuniQ, a reinforcement learning-based system that selects compilation passes at each pipeline stage, adapting to circuit, backend, and current noise profile. TuniQ introduces several novel design components like a dual-encoder for stage-aware representation, shaped rewards for cross-stage credit assignment, and dynamic action masking for valid compilation. Evaluated across diverse quantum workloads on multiple IBM Quantum Cloud processors, TuniQ improves fidelity and reduces compilation time over the state-of-the-art IBM Qiskit transpiler, generalizes across backends without retraining, and scales strongly to utility-scale circuits with growing advantage.

We study parity features as representations that can be evaluated entirely classically once the binary or quantized input representation and parity words are fixed, particularly when labels depend on higher-order feature interactions or when discrete inference interfaces support perturbation robustness. A parity feature is a signed product over selected bits of a binary input: once the participating bits are known, evaluation requires no quantum resources. Reaching a useful parity representation requires solving two challenges. When the input is parity-ready (a meaningful binary string), the challenge is basis discovery: selecting useful parity words from a combinatorial search space. Otherwise, the challenge is encoding: constructing a binary vector on which parity computation is meaningful. We use hybrid quantum-classical training pipelines to address these: learnable Pauli word selection for basis discovery, learned projection encodings for continuous embeddings, and sPQC-Parity for discrete inputs. On three native-binary parity tasks with 5-10 qubits, the learned parity basis improves mean accuracy by 23.9% to 41.7% over logistic-regression and support-vector baselines. A model comparison shows that the improvement comes primarily from discovering the right parity basis, rather than from quantum moment computation at inference. On five continuous text benchmarks, learned projection recovers much of the loss introduced by dimensionality reduction and fixed binarization, exceeding the full continuous baseline on CR, SST-2, and SST-5. On three encoding-limited discrete datasets, when compared with PCA-bin as the baseline, sPQC-Parity reaches 94.6% improvement on mushroom, 3.0% on splice, and matches PCA-bin on promoter. We also analyze inference robustness under binary or quantized inference, where rounding gives exact invariance below half the quantization step.

We introduce Unitaria, a Python library that brings the simplicity of classical linear algebra toolkits such as NumPy and SciPy to the implementation of quantum algorithms based on block encodings, a general-purpose abstraction in which a matrix is embedded as a sub-block of a larger unitary operator. Their implementation has so far required deep knowledge of low-level circuit construction, which Unitaria aims to eliminate. The library provides a composable, array-like interface through which users can define block encodings of matrices and vectors, combine them through standard operations such as addition, multiplication, tensor products, and the Quantum Singular Value Transformation, and extract the resulting quantum circuits automatically. A key feature is a matrix-arithmetic evaluation path in which every operation can be computed directly on encoded vectors and matrices without dependence on ancilla qubits or circuit simulation. This enables correctness verification and classical simulation that scale well beyond what state vector simulation permits and also allows resource estimation, including gate counts, qubit counts, and normalization constants, without executing any circuit. Together, these capabilities allow researchers to develop, verify, and analyze quantum linear algebra algorithms today, ahead of the availability of error-corrected hardware. Unitaria is open source and available at https://github.com/tequilahub/unitaria.

Hybrid quantum-classical algorithms can help mitigating the physical limitations of current quantum devices, particularly the low qubit count and the reduced topological connectivity. In this paper, we propose a hybrid technique to solve a well-known NP-hard optimization problem: the Traveling Salesperson Problem (TSP). Our approach is based on a graph contraction technique that removes most of the dimensionality of the original problem instance, producing a sub-TSP of a size suitable to be efficiently solved by a quantum device. The performance of our approach is first demonstrated on classical quantum simulation using Path Integral Monte Carlo, and then run on a D-Wave quantum annealer.

Scalable qubit mapping and routing remain major bottlenecks in quantum compilation, especially for Trapped-Ion Quantum Charge-Coupled device (TI-QCCD) architectures, where qubit interactions require physically shuttling ions under strict movement, congestion, and trap-capacity constraints. We present a compilation framework built around the position graph abstraction, a unified representation of executable locations, movement paths, and routing constraints that enables heuristic mappers to operate directly on shuttling-based hardware. Using this abstraction, we accelerate the SWAP-based BidiREctional heuristic search (SABRE) by implementing relative move scoring, which caches repeated heuristic move evaluations that arise during search, and memoized congestion resolution, which speeds up the resolution of repeated congestion. This optimization removes redundant computation without changing routing/shuttling decisions, improving the scalability of SABRE-based methods on TI-QCCD systems. Our results show that combining an architecture-aware abstraction with memoized heuristic evaluation yields a practical and effective path toward scalable qubit mapping and routing across heterogeneous quantum architectures.

Current and near-term quantum hardware is constrained by limited qubit counts, circuit depth, and the high cost of repeated measurements. We address these challenges for solid-state Hamiltonians by introducing a logarithmic-qubit encoding that maps a system with N physical sites onto only &amp;#x2308; log 2 &amp;#x2061; N &amp;#x2309; qubits while maintaining a clear correspondence with the underlying physical model. Within this reduced register, we construct a compatible variational circuit and a Gray-code-inspired measurement strategy whose number of global settings grows only logarithmically with system size. To quantify the overall hardware load, we introduce a volumetric efficiency metric that combines the number of qubits, circuit depth, and the number of measurement settings into a single measure, expressing the overall computation costs. Using this metric, we show that the total space--time sampling volume required in a variational loop can be reduced dramatically from N 2 to ( log &amp;#x2061; N ) 3 for a hardware-efficient ansatz, allowing an exponential reduction in time and size of the quantum hardware. These results demonstrate that large, structured solid-state Hamiltonians can be simulated on substantially smaller quantum registers with controlled sampling overhead and manageable circuit complexity, extending the reach of variational quantum algorithms on near-term devices.

Quantum compilers sit between an algorithm's theoretical promise and what executes on physical hardware. Existing benchmarks report aggregate post-transpilation metrics but cannot attribute where fidelity is lost within the compilation pipeline. We present HBR decomposition, a per-phase fidelity attribution model that quantifies relative fidelity loss across High-level structural decomposition (H), Basis translation (B), and Routing (R). We evaluate three production SDKs (Qiskit, PennyLane, TKET) across eight algorithms on two backend topologies: IBM Heron (heavy-hex) and IonQ Forte (all-to-all). The dominant compiler bottleneck is strongly circuit-class dependent: Routing accounts for up to 60% of relative fidelity loss in search-class circuits, while synthesis dominates Hamiltonian simulation workloads. Early synthesis choices amplify or compress downstream routing overhead depending on circuit connectivity. SDK rankings at diagnostic optimization level (opt=0) reverse at production levels (opt=2) for deep circuits, showing that stagewise diagnostics and production results answer different questions. HBR correctly predicts SDK rank ordering across noisy simulations (8 circuits x 3 SDKs x 2 tiers) and real IBM Fez hardware executions, revealing stage-specific bottlenecks that are not observable through aggregate compiler benchmarks.

Plasma simulations are among the most computationally demanding scientific workloads, combining high-dimensional kinetic evolution, particle-mesh coupling, field solves, and data-intensive communication. As general-purpose processor scaling slows, post-Moore technologies are being explored to address bottlenecks in data movement, memory access, and power consumption. This paper provides a community perspective on the role of these technologies in plasma simulation, assessing three major classes: reconfigurable and data-path accelerators, non-von Neumann architectures, and quantum computing. Each is evaluated, in a co-design approach, against representative plasma workloads spanning particle-in-cell, continuum Vlasov, gyrokinetic, fluid/MHD, hybrid, and warm dense matter methods. We find that no single technology can replace existing HPC platforms. Instead, three tiers of opportunity emerge: FPGA-class and data-path accelerators offer near-term kernel offload and workflow-level data services, non-von Neumann architectures represent medium-term directions for operator-level acceleration, and quantum computing, although the least mature, is potentially the most disruptive for warm dense matter and inertial confinement fusion microphysics. We outline best practices for selective adoption and identify focused demonstrators, benchmarking, and modular software ecosystems as immediate community priorities.

To overcome the limitations of classical partially connected Boltzmann machines and mainstream quantum Boltzmann machines (QBMs), this work extends the conventional circuit of the quantum approximate optimization algorithm (QAOA) to a bilevel optimization architecture and proposes a fully connected QBM. The inner-loop training simulates positive phase energy minimization based on the computational process of the conventional QAOA circuit, whereas the outer-loop training simulates negative phase contrastive divergence learning by optimizing the structural parameters of the target Hamiltonian. It is found that, first, the model exhibits superior performance using only a single layer (p=1) in the QAOA circuit, with an average probability of 0.9559 in measuring the target quantum state under noiseless conditions. Second, the model exhibits notable noise robustness. Under the typical noise level of current mainstream commercial quantum computing devices, the average probability of measuring the target quantum state reaches 0.6047; when the noise rises to a more stringent level with doubled intensity, this probability remains at 0.3859. In both scenarios, the target quantum state maintains the highest measurement probability among all detected states, with a value several times higher than that of the second-ranked state. This indicates that the model retains strong robustness even when noise meets or exceeds the upper limit of current mainstream commercial quantum computing devices. Third, under a block-by-block learning strategy with p=1 and only 10 measurement shots, the model consistently generates the target "qubit" grid image regardless of noise interference, demonstrating strong robustness in image generation.

Abstract Bosonic Gaussian states are ubiquitous in quantum optics and condensed matter physics. While they are efficiently handled within the Gaussian formalism, sampling requires calculating amplitudes in the boson occupation basis. This step, however, is hindered by a significant bottleneck due to the hafnian. We present an efficient algorithm that converts pure bosonic Gaussian states into matrix product states (MPSs), thereby establishing a versatile tool for probing bosonic Gaussian systems in settings where direct Gaussian-formalism-based calculations become inefficient. Our method combines a Gaussian singular value decomposition with a projected-creation-operator mapping that constructs local MPS tensors without computing hafnians. Benchmarking on covariance matrices from the Jiuzhang 2.0 and Jiuzhang 4.0 Gaussian boson sampling experiments demonstrates substantial speedups over previous tensor-network approaches in the low-entanglement regime relevant to lossy devices. The method provides a scalable classical simulation framework for bosonic Gaussian states with limited entanglement. In this regime, a target accuracy can be achieved with a bond dimension that remains computationally tractable, thereby extending the applicability of MPS-based methods to a broad range of bosonic systems.

Quantum annealing is a computational paradigm in which optimisation problems are mapped onto the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming a simple initial Hamiltonian into one whose ground state encodes the solution, the system traverses a complex landscape via a combination of quantum fluctuations, tunnelling processes, and dissipative dynamics. Unlike gate-based quantum computing, quantum annealing is a specialised and near-term approach aimed primarily at discrete optimisation and sampling tasks. While it is not expected to provide polynomial-time solutions to NP-hard problems in the worst case, it offers a physically motivated heuristic for navigating rugged energy landscapes that arise across science and engineering. Modern quantum annealers realise programmable spin systems with thousands of qubits, placing them among the largest controllable quantum devices currently available. As a result, their significance extends beyond optimisation: they also function as experimental platforms for studying non-equilibrium many-body quantum dynamics in regimes that are difficult to access using classical simulation. In this review we present an accessible introduction to the principles of quantum annealing, describe the main hardware platforms and algorithmic techniques, and analyse how tunnelling, spectral gaps, and open-system effects shape computational performance. We survey applications ranging from optimisation and machine learning to quantum simulation and many-body physics, and discuss the central challenges in benchmarking, scaling, and control. These perspectives position quantum annealing as a distinctive framework at the interface of optimisation, stochastic sampling, and programmable quantum dynamics, with a role that is complementary to both classical algorithms and gate-based quantum computing.

We introduce a hybrid quantum-classical pipeline, based on neutral-atom reservoir computing, for medical image classification, focusing on the binary classification task of polyp detection. To deal effectively with the high dimensionality, we integrate a guided auto-encoder. This pipeline learns compact and discriminative representations of image data that are also well-suited for quantum reservoir computing. A key challenge in such systems is the non-differentiable nature of quantum measurements, which creates a 'gradient barrier' for standard training. We overcome this barrier by incorporating a differentiable surrogate model that emulates the quantum layer, enabling end-to-end backpropagation through the entire system. This guided training process is jointly optimized for classification accuracy and for faithful image recovery from the auto-encoder. The learned latent representations are encoded as pulse detuning parameters within a Rydberg Hamiltonian, and quantum embeddings are subsequently obtained through expectation values. These embeddings are then passed to a linear classifier. Our simulations show that this method outperforms some traditional approaches that use PCA or unguided autoencoders. We also conduct ablation studies to assess the impact of various quantum and training parameters, demonstrating the robustness and flexibility of our proposed pipeline for real-world medical imaging applications, even in the current NISQ era.

In this paper, we develop the resource theory of quantum secret key. Operating under the assumption that entangled states with zero distillable key do not exist, we define the key cost of a quantum state, and device. We study its properties through the lens of a quantity that we call the key of formation. The main result of our paper is that the regularized key of formation is an upper bound on the key cost of a quantum state. The core protocol underlying this result is privacy dilution, which converts states containing ideal privacy into ones with diluted privacy. Next, we show that the key cost is bounded from below by the regularized relative entropy of entanglement, which implies the irreversibility of the privacy creation-distillation process for a specific class of states. We further focus on mixed-state analogues of pure quantum states in the domain of privacy, and we prove that a number of entanglement measures are equal to each other for these states, similar to the case of pure entangled states. The privacy cost and distillable key in the single-shot regime exhibit a yield-cost relation, and basic consequences for quantum devices are also provided. Importantly, our results presented here will remain valid even if entangled states with zero distillable key were shown to exist.

We show the 2-Local Stoquastic Hamiltonian problem on a 2D square qubit lattice is StoqMA-complete. We achieve this by extending the spatially sparse circuit construction of Oliveira and Terhal, as well as the perturbative gadgets of Bravyi, DiVincenzo, Oliveira, and Terhal. Our main contributions demonstrate StoqMA circuits can be made spatially sparse and that geometrical, stoquastic-preserving, perturbative gadgets can be constructed, without an increase to particle dimension.

This paper aims to devise the shape of the external electromagnetic field that drives the spin dynamics of radical pairs to a quantum coherent state through maximization of the triplet-born singlet yield in biochemical reactions. The model is a Schrödinger system with spin Hamiltonians given by the sum of Zeeman interaction and hyperfine coupling interaction terms. We introduce a one-parameter family of optimal control problems by coupling the Schrödinger system to a control field through filtering equations for the electromagnetic field. Fréchet differentiability and the Pontryagin Maximum Principle in Hilbert space are proved, and the bang-bang structure of the optimal control is established. A new iterative Pontryagin Maximum Principle (IPMP) method for the identification of the bang-bang optimal control is developed. Numerical simulations based on IPMP and the gradient projection method (GPM) in Hilbert spaces are pursued, and the convergence, stability, and the regularization effect are demonstrated. Comparative analysis of filtering with regular optimal electromagnetic field versus non-filtering with bang-bang optimal field ( Abdulla et al, Quantum Sci. Technol.,&amp;#xA0; 9 , 4, 2024 ) demonstrates that the change of the maxima of the singlet yield is less than 1%. The results open a venue for a potential experimental work on magnetoreception as a manifestation of quantum biological phenomena.

Abstract A Gaussian boson sampler (GBS) is a special-purpose quantum computer that can be practically realized at a large scale in optics. Here we report on experiments in which we used a frequency-multiplexed GBS with &gt; 400 modes as a quantum reservoir. We evaluated the accuracy of our GBS-based reservoir computer on a variety of benchmark tasks. We found that when the system was given access to the correlations between measured modes of the GBS, the achieved accuracies were the same or higher than when it was only given access to the mean photon number in each mode—and in several cases the advantage in accuracy from using the correlations was greater than 20 percentage points. This provides experimental evidence in support of theoretical predictions that access to correlations enhances the power of quantum reservoir computers. We also tested our reservoir computer when operating the reservoir with various sources of classical rather than quantum light and found that using squeezed light consistently resulted in the highest accuracies. Our work experimentally establishes that a GBS can be an effective quantum reservoir and provides a practical platform for experimentally exploring the role of quantumness and correlations in quantum machine learning at very large system sizes.

Abstract Simulating vibronic spectra is a central task in physical chemistry, offering insight into important properties of molecules. Recently, it has been experimentally demonstrated that photonic platforms based on Gaussian boson sampling (GBS) are capable of performing these simulations. However, whether an actual GBS approach is required depends on the molecule under investigation. To develop a better understanding on the requirements for simulating vibronic spectra, we explore connections between theoretical approximations in physical chemistry and their photonic counterparts. Mapping these approximations into photonics, we show that for certain molecules the GBS approach is unnecessary. We place special emphasis on the linear coupling approximation, which in photonics corresponds to sampling from multiple coherent states. By implementing this approach in experiments, we demonstrate improved similarities over previously reported GBS results for formic acid and identify the particular attributes that a molecule must exhibit for this, and other approximations, to be valid. These results highlight the importance in forming deeper connections between traditional methods and photonic approaches.

Abstract Thermoelectricity is generally understood as a classical effect emerging from energy-dependent transport asymmetries. Here, we uncover a purely quantum mechanism, where a superconducting S-I-S’ tunnel junction in thermal equilibrium develops a nonlinear bipolar thermoelectric response owing to the dynamical Coulomb blockade and the emission-absorption imbalance of a cold electromagnetic bath. Two representative environments are analysed, revealing Seebeck coefficients up to 100 μV/K for realistic junction parameters. Because the response directly reflects the spectral properties of the surrounding environment, our results suggest that bipolar quantum thermoelectricity could provide a new route for spectroscopic sensing of electromagnetic modes and for designing low-temperature thermoelectric devices with environmentally engineered performance.

Emerging quantum sensors are increasingly envisioned as components of hybrid quantum-classical high-performance computing, enabling new capabilities in scientific, cyber-physical, and machine-learning pipelines. However, their practical utility is limited by environmental decoherence, which degrades sensing reliability. While dynamical decoupling (DD) pulse sequences can mitigate this, standard methods are often suboptimal in the presence of realistic noise. We present SpinTune, a reinforcement learning software approach that autonomously discovers adaptive, piecewise DD sequences tailored to specific environments. Using a simulation model of a Carbon-13 spin bath, we show that SpinTune significantly outperforms standard DD sequences in preserving coherence.

State conversion is a fundamental task in quantum information processing. Quantum resource theories allow for analyzing and bounding conversions that use restricted sets of operations. In the context of continuous-variable systems, state conversions restricted to Gaussian operations are crucial for both fundamental and practical reasons, particularly in state preparation and quantum computing with bosonic codes. However, previous analysis did not consider the relevant case of approximate state conversion. In this work, we introduce a framework for assessing approximate Gaussian state conversion by extending the stellar rank to the approximate stellar rank, which serves as an operational measure of non-Gaussianity. We derive bounds for Gaussian state conversion and distillation under approximate and probabilistic conditions, yielding new no-go results for non-Gaussian state preparation and enabling a reliable assessment of the performance of Gaussian conversion protocols. We also provide an open-source Python library to compute stellar-rank-related quantities and to assess Gaussian conversion.

Graph states are entangled states that are essential for quantum information processing. As experimental advances enable the realization of large-scale graph states, efficient fidelity estimation methods are crucial for assessing their robustness against noise. However, calculations of exact fidelity become intractable for large systems due to the exponential growth in the number of stabilizers. In this work, we show that the fidelity between any ideal graph state and its noisy counterpart under IID Pauli noise can be mapped to the partition function of a classical spin system, enabling efficient computation via statistical mechanical techniques. Using this approach, we analyze the fidelity for regular graph states under depolarizing noise and uncover the emergence of phase transitions in fidelity between the pure-state regime and the noise-dominated regime. Specifically, in 2D, phase transitions occur only when the degree satisfies d &amp;#x2265; 6 , while in 3D they already appear at d &amp;#x2265; 5 . However, for graph states with excessively high degree, such as fully connected graphs, the phase transition disappears. Robustness of graph states against noise is thus determined by their connectivity and spatial dimensionality. Graph states with lower degree and/or dimensionality, which exhibit a smooth crossover, demonstrate greater robustness, while highly connected or higher-dimensional graph states are more fragile. Extreme connectivity, as the fully connected graph state possesses, restores robustness. Furthermore, we show that the fidelity can be rewritten in the form of the partition function of a constraint-percolation problem. Within this picture, we discuss the qualitative difference between 2D regular graph states with d = 6 and d = 5 regarding the presence or absence of a phase transition, as well as the suppressed critical behavior of fully connected graph states.

Quantum circuit simulation is paramount to the verification and optimization of quantum algorithms, and considerable research efforts have been made towards efficient simulators. While circuits often contain high-level gates such as oracles and multi-controlled X ( C k X ) gates, existing simulation methods require compilation to a low-level gate-set before simulation. This, however, increases circuit size and incurs a considerable (typically exponential) overhead, even when the number of high-level gates is small. Here we present a gadget-based simulator which simulates high-level gates directly, thereby allowing to avoid or reduce the blowup of compilation. Our simulator uses a stabilizer decomposition of the magic state of non-stabilizer gates, with improvements in the rank of the magic state directly improving performance. We then proceed to establish a small stabilizer rank for a range of high-level gates that are common in various quantum algorithms. Using these bounds in our simulator, we improve both the theoretical complexity of simulating circuits containing such gates, and the practical running time compared to standard simulators found in IBM's Qiskit Aer library. We also derive exponential lower-bounds for the stabilizer rank of some gates under common complexity-theoretic hypotheses. In certain cases, our lower-bounds are asymptotically tight on the exponent.

Calculating the quantum weight enumerator polynomial (WEP) is a valuable tool for characterizing quantum error-correcting (QEC) codes, but it is computationally hard for large or complex codes. The Quantum LEGO (QL) framework provides a tensor network approach for WEP calculation, in some cases offering superpolynomial speedups over brute-force methods, provided the code exhibits area law entanglement, that a good QL layout is used, and an efficient tensor network contraction schedule is found. We analyze the performance of a hyper-optimized contraction schedule framework across QL layouts for diverse stabilizer code families. We find that the intermediate tensors in the QL networks for stabilizer WEPs are often highly sparse, invalidating the dense-tensor assumption of standard cost functions. To address this, we introduce an exact, polynomial-time Sparse Stabilizer Tensor (SST) cost function based on the rank of the parity check matrices for intermediate tensors. The SST cost function correlates perfectly with the true contraction cost, providing a significant advantage over the default cost function, which exhibits large uncertainty. Optimizing contraction schedules using the SST cost function yields substantial performance gains, achieving up to orders of magnitude improvement in actual contraction cost compared to using the dense tensor cost function. Furthermore, the precise cost estimation from the SST function offers an efficient metric to decide whether the QL-based WEP calculation is computationally superior to brute force for a given QL layout. These results, enabled by PlanqTN, a new open-source QL implementation, validate hyper-optimized contraction as a crucial technique for leveraging the QL framework to explore the QEC code design space.

Quantum hypergraph states form a generalisation of the graph state formalism that goes beyond the pairwise (dyadic) interactions imposed by remaining inside the Gaussian approximation. Networks of such states are able to achieve universality for continuous variable measurement based quantum computation with only Gaussian measurements. For normalised states, the simplest hypergraph states are formed from k -adic interactions among a collection of k harmonic oscillator ground states. However such powerful resources have not yet been observed in experiments and their robustness and scalability have not been tested. Here we develop and analyse necessary criteria for hypergraph nonclassicality based on simultaneous nonlinear squeezing in the nullifiers of hypergraph states. We put forward an essential analysis of their robustness to realistic scenarios involving thermalisation or loss and suggest several basic proof-of-principle options for experiments to observe nonclassicality in hypergraph states.

We study higher order quantum maps in the context of a *-autonomous category of affine subspaces. We show that types of higher order maps can be identified with certain Boolean functions that we call type functions. By an extension of this identification, the algebraic structure of Boolean functions is inherited by some sets of quantum objects including higher order maps. Using the Mobius transform, we assign to each type function a poset whose elements are labelled by subsets of indices of the involved spaces. We then show that the type function corresponds to a comb type if and only if the poset is a chain. We also devise a procedure for decomposition of the poset to a set of basic chains from which the type function is constructed by taking maxima and minima of concatenations of the basic chains in different orders. On the level of higher order maps, maxima and minima correspond to affine mixtures and intersections, respectively.

The Feedback-based Algorithm for Quantum Optimization (FALQON) offers a deterministic alternative to variational quantum algorithms by bypassing classical optimization loops. However, maintaining convergence on large problem instances often requires restricting the time step, necessitating quantum circuit depths that exceed Noisy Intermediate-Scale Quantum (NISQ) hardware capabilities. This paper investigates the parameter transferability of second-order FALQON applied to the Max-Cut problem on 3-regular graphs. Through numerical experiments evaluating quantum circuits up to 16 layers on graphs up to 24 nodes, we demonstrate a highly advantageous scaling behavior: transferring feedback parameters optimized on small instances to larger target graphs yields significantly higher approximation ratios than natively optimizing the parameters directly on the larger graphs. This performance advantage arises because parameters trained on smaller instances can safely adopt aggressively larger time steps. By offloading the expensive parameter discovery phase to small-scale instances, this transfer strategy simultaneously reduces computational overhead and enhances the approximation ratio, thereby bringing FALQON closer to practical viability on near-term quantum architectures.

Performing multiple computations within the same system, without spatial or temporal separation of tasks, requires encoding multiple data items into a well-defined physical state. The most widely explored mechanism for such encoding is the superposition of physical states representing computational states. However, superposition requires the system to be linear, which significantly limits the set of achievable operations. We show that system symmetries provide an alternative mechanism for encoding multiple computational states. Notably, this mechanism also applies to nonlinear systems and therefore does not impose inherent limits on computed functions. Using the evaluation of Boolean functions as an example, we show that a relaxed spin network driven by the V-2 model supports this mechanism. We relate the resulting simultaneous computations enabled by symmetry-induced parallelism to properties of the evaluated functions. We demonstrate symmetry-induced parallelism for a logical AND/OR gate and an N-bit adder.

Abstract Simulating correlated materials on present-day quantum hardware remains challenging due to limited quantum resources. Quantum embedding methods offer a promising route by reducing computational complexity through the mapping of bulk systems onto effective impurity models, allowing more feasible simulations on pre- and early-fault-tolerant quantum devices. This work develops a quantum-classical embedding framework based on the ghost Gutzwiller approximation to enable quantum-enhanced simulations of ground-state properties and spectral functions of correlated electron systems. Circuit complexity is analyzed using an adaptive variational quantum algorithm on a statevector simulator, applied to the infinite-dimensional Hubbard model with increasing ghost mode numbers from 3 to 5, resulting in circuit depths growing from 16 to 104. Noise effects are examined using a realistic error model, revealing significant impact on the spectral weight of the Hubbard bands. To mitigate these effects, the Iceberg quantum error detection code is employed, achieving up to 40% error reduction in simulations. Finally, the accuracy of the density matrix estimation and the derived spectral function is benchmarked on IBM and Quantinuum quantum hardware, featuring distinct qubit-connectivity and employing multiple levels of error mitigation techniques.

Quantum-classical interfaces (QCIs) for fault-tolerant quantum computing must manage simultaneous, real-time decoding across thousands to millions of logical qubits. Scaling these architectures necessitates sharing expensive decoding resources among logical qubits, which introduces severe resource contention within the QCI. While resolving these bottlenecks through efficient resource distribution remains a persistent challenge, lightweight predecoding holds promise to alleviate strain on shared decoding components by decreasing average latency and decoder usage. Notably, research into both decoder allocation and predecoding has been strictly confined to the surface code. With the growing emphasis on general quantum low-density parity-check (qLDPC) codes, slower decoding speeds will intensify resource contention, while the inherent complexity of these codes will render manual predecoder design unfeasible. To address this gap, we introduce an automated framework designed to generate predecoders for arbitrary qLDPC codes. These automatically constructed predecoders autonomously process over 90% of the decoding workload, cutting overall decoder utilization by up to 3,963x. This includes a reduction of up to 72.71% in computationally demanding ordered statistics decoding (OSD). Furthermore, we detail a highly efficient, pipelined hardware design that allows for the concurrent decoding of approximately 1,200 bivariate bicycle (BB) code logical qubits using a single FPGA. When implemented as a cryogenic ASIC, the architecture scales to support between 36,000 and 360,000 BB code logical qubits, operating within a 1.5 W power limit at 4 K.

Quantum error detection can produce unbiased expectation values that exponentially converge to noiseless results as the code distance is increased. Despite this, its performance as an error mitigation technique is relatively understudied on quantum hardware because of its two main drawbacks: (i) the number of samples increases exponentially in the circuit depth/noise level, and (ii) the classical processing generally grows exponentially in the code distance, though exceptions exist. Additionally, the constant (but often large) overhead of embedding the code and logical operations on hardware can make accuracy worse instead of better. In this work, we seek to provide a clear picture of these opportunities and challenges for scaling quantum error detection on hardware. We do so by performing a detailed benchmarking study on real and simulated noisy quantum computers, using the repetition code and triangular color code for memory experiments and logical computations with up to $74$ physical qubits. In addition to these benchmarks, we estimate the pseudothreshold of codes to map the frontier of error detection on current and future quantum computers. Despite the challenges, our results show strong promise for scaling quantum error detection on hardware.

We present an experimental study of energy-to-solution (ETS) of hybrid quantum-classical applications, enabled by direct instrumentation of power consumption of a Forte Enterprise trapped-ion quantum processor. We apply this methodology to a hybrid quantum-classical pipeline for quantum fine-tuning of foundational AI models, and validate the approach end-to-end on quantum hardware. Despite noise and limited qubit counts, the resulting models achieve accuracy competitive with and exceeding classical baselines such as logistic regression and support vector classifiers. Our results show that QPU energy consumption scales approximately linearly with qubit number for shallow circuits, while classical simulation exhibits exponential scaling, indicating a break-even for ETS around 34 qubits. The classification error improvement of the best quantum fine-tuned model over the best classical fine-tuned model considered in this study is around 24%. We further contextualize these findings with comparisons to tensor network methods. This work establishes energy-to-solution as a measurable and scalable metric for evaluating quantum applications and provides experimental evidence of favorable energy-accuracy trade-offs.

Quantum software development has largely focused on algorithms, with limited attention to software architecture. As computing moves toward hybrid quantum-classical systems, this gap limits scalability, reusability, and engineering rigor. This study introduces a component-based quantum software architecture framework (QSAF) for hybrid quantum-classical software systems, enabling developers to transition from circuit-level design to system-level reasoning. We identified 34 reusable quantum circuit primitives across seven functional categories and reinterpreted them as architectural components with explicit interfaces and design-relevant constraints. These components are further characterized using non-functional dimensions such as circuit depth, error sensitivity, and information flow, enabling a structured analysis of design trade-offs. The proposed QSAF framework establishes a multi-level abstraction hierarchy linking quantum gates, circuit primitives, algorithmic structures, and hybrid system architectures. Through this approach, common workflows, particularly hybrid quantum-classical workflows such as variational quantum algorithms, can be systematically decomposed, compared, and optimized. By making the architectural structure and trade-offs explicit, this study provides a foundation for quantum software engineering, supporting modular design, reuse, and informed architectural decision-making in quantum application development.

The shift to electric freight is accelerating, and its economics hinge on a planning problem that conventional routing software was not designed to handle. Research conducted by Einride, a technology company building the infrastructure for electric and autonomous freight, alongside Fraunhofer and Rewe, found that optimizing electric fleet operations from the ground up reduced fleet-level total cost of ownership by 8–13%, compared to roughly 3% for straightforward 1:1 replacement of diesel trucks with EVs. Electric fleets introduce charging schedules, energy constraints, and route interdependencies that make planning substantially more complex than conventional trucking. That complexity, managed well, is where the economic advantage lives.

Partitioning transportation networks into balanced and spatially coherent traffic zones is a fundamental yet computationally challenging task in intelligent transportation systems. The resulting optimization problem exhibits dense interactions among decision variables and can be formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model. While quantum optimization naturally aligns with such quadratic energy representations, current noisy intermediate-scale quantum hardware imposes limitations on problem size, connectivity, and circuit reliability. This paper proposes an impact-driven hybrid quantum--classical optimization framework for traffic zone partitioning that bridges transportation-scale optimization models and practical gate-based quantum processors. Instead of static geographic decomposition, the method estimates the energy impact of decision variables and selectively assigns quantum computation to influential subproblems while a classical coordination loop maintains global feasibility. The framework is implemented using the Iskay optimizer and evaluated on the IBM Quantum System One backend. Experiments compare direct quantum optimization, classical iterative SubQUBO refinement, and the proposed hybrid approach. Results show that impact-guided decomposition improves convergence behavior and produces more coherent spatial partitions relative to classical refinement, while remaining consistent with hardware constraints. Although the hybrid method does not outperform the best direct quantum solution, it demonstrates a practical pathway toward scalable hybrid optimization for transportation applications under current quantum hardware conditions.