Quantum Computing Research Archive

Algorithms & Theory

Interactive verification protocols for quantum computations allow to build trust between a client and a service provider, ensuring the former that the instructed computation was carried out faithfully. They come in two variants, one without quantum communication that requires large overhead on the server side to coherently implement quantum-resistant cryptographic primitives, and one with quantum communication but with repetition as the only overhead on the service provider's side. Given the limited number of available qubits on current machines, only quantum communication-based protocols have yielded proof of concepts. In this work, we show that the repetition overhead of protocols with quantum communication can be further mitigated if one examines the task of operating a quantum machine from the service provider's point of view. Indeed, we show that the test rounds data, whose collection is necessary to provide security, can indeed be recycled to perform continuous monitoring of noise model parameters for the service provider. This exemplifies the versatility of these protocols, whose template can serve multiple purposes and increases the interest in considering their early integration into development roadmaps of quantum machines.

Quantum algorithms require encoding classical vectors as quantum states, a step known as amplitude encoding. General-purpose routines produce circuits with O(2^m) gates for vectors of length N = 2^m, for an m-qubit register. However, vectors arising in scientific and engineering applications often exhibit mathematical structure that admits far more efficient encoding. Theoretical work over the last decade has established efficient circuits for several structured vector classes, but without open-source implementations. We present PyEncode, an open-source Python library that implements this body of theory in a unified framework. It covers ten exact pattern families: sparse, step, square, Walsh, Fourier, geometric, Hamming, staircase, Dicke, and polynomial. A function encode maps each pattern to a verified Qiskit circuit, with no vector materialization and no approximation; for example, encode(SPARSE([(19, 1.0)]), N=64) encodes the vector e_19 of length N = 64. Sparse, step, Walsh, Hamming, and staircase patterns require O(m) gates; square and Fourier patterns require O(m^2); Dicke states D^m_k require O(k(m-k)), that denotes uniform superpositions over indices of Hamming weight k; degree-d polynomials require O(m^(d+1)). A companion predict_gates function estimates transpiled gate counts without synthesis, and a reverse-lookup utility match_vector identifies which family best fits a given numerical vector. Three composition primitives are supported: SUM for weighted superpositions, PARTITION for ancilla-free composition of disjoint-support patterns, and TENSOR for separable states over disjoint subregisters. For amplitude vectors outside these exact families, PyEncode also provides a matrix product state (MPS) loader, encode_mps for approximate vector encoding. The library is available at https://github.com/UW-ERSL/PyEncode.

This work presents a novel tensor network algorithm for solving Quadratic Unconstrained Binary Optimization (QUBO) problems, Quadratic Unconstrained Discrete Optimization (QUDO) problems, and Tensor Quadratic Unconstrained Discrete Optimization (T-QUDO) problems. The proposed algorithm is based on the MeLoCoToN methodology, which solves combinatorial optimization problems by employing superposition, imaginary time evolution, and projective measurements. Additionally, two different approaches are presented to solve QUBO and QUDO problems with k-neighbors interactions in a lineal chain, one based on 4-order tensor contraction and the other based on matrix-vector multiplication, including sparse computation and a new technique called "Waterfall". Furthermore, the performance of both implementations is compared with a quadratic optimization solver to demonstrate the performance of the method, showing advantages in several problem instances.

Both Superconducting and Ion-Trap are leading quantum architectures common in the current landscape of the quantum computing field, each with distinct characteristics and operational constraints. Understanding and measuring the underlying \underline{quantumness} of these devices is essential for assessing their readiness for practical applications and guiding future progress and research. Building on earlier work (Meirom, Mor and Weinstein Arxiv 2505.12441), we utilize a benchmarking strategy applicable for comparing these two architectures by measuring "quantumness" directly on optimal sub-chips. Distinct from existing metrics, our approach employs rigorous binary fidelity thresholds derived from the classical limits of state transfer. This enables us to definitively establish quantum advantage of a designated sub-region. Here we apply this quality assurance methodology to platforms from both technologies. This comparison provides a protocol-based evaluation of quantumness advantage, revealing not only the strengths and weaknesses of each tested chip and its sub-chips but also offering a common language for their assessment. By abstracting away technical differences in the final result, we demonstrate a benchmarking strategy that bridges the gap between disparate quantum-circuit technologies, enabling fair performance comparisons and establishing a critical foundation for evaluating future claims of quantum advantage. This work was made possible by policies of two companies who enable independent and objective assessment on their quantum computers and sub-chips. In the name of science, we encourage other companies to emulate the independent qubit availability and the fair pricing which allow researchers to preform such assessments.

The gaze-and-pinch framework offers a high-fidelity interaction modality for spatial computing in virtual reality (VR), yet it remains vulnerable to coordination errors--timing misalignments between gaze fixation and pinch gestures. These errors are categorized into two types: late triggers (gaze leaves a target before pinch) and early triggers (pinch before gaze arrival on target). While late triggers are well-studied, early triggers lack robust solutions. We investigate two heuristics--STICKY selection (temporal buffer) and MAGNETIC selection (spatial field)--to mitigate these errors. A within-subjects study (N = 9) on the Samsung Galaxy XR evaluated these heuristics against a baseline. Findings indicate that while throughput and selection time remained stable, the heuristics fundamentally shifted user behavior and significantly reduced errors during selection. Notably, MAGNETIC selection induced an "offloading" effect where users traded precision for speed. Additionally, the heuristics reclassified ambiguous failures as explainable coordination errors. We provide recommendations for selection heuristics that enhance interaction speed and cognitive agency in virtual reality.

In finance, assessing the creditworthiness of loan applicants requires lenders to cluster borrowers using rating scales. Financial institutions must define the scales in compliance with strict institutional constraints, resulting in solving a complex combinatorial constrained optimization problem. This contribution studies how to solve this problem using a Quadratic Unconstrained Binary Optimization (QUBO) model, a formulation suitable for quantum hardware. We validate this approach by testing the proposed formulation with classical heuristics. We then benchmark the results against a brute-force method to demonstrate consistent solution quality and highlight the framework's suitability for more complex scenarios.

A large-scale quantum circuit can be partitioned into multiple subcircuits through circuit cutting, where each subcircuit is executed multiple times and the expectation value of the original circuit is reconstructed by classical post-processing from their measurement (sampling) results. In this process, appropriate cut locations are identified after the user-designed quantum circuit, including multi-qubit gates that act on three or more qubits, has been decomposed into single-qubit gates and two-qubit gates such as the CNOT gate. Here, we present a method for reducing the sampling overhead, which refers to the increase in the number of samples required due to the cutting process, by modifying the decomposition strategy of multi-qubit gates. Using MCX and CCCX gates as representatives of multi-qubit gates, we demonstrate that the proposed decomposition method, which introduces a small number of ancilla qubits according to the identified cut locations, effectively decreases the sampling overhead.

Superconducting Single Flux Quantum (SFQ) logic offers a promising platform for ultra-low-power, high-frequency computing. However, their pulse-based nature poses challenges for scalable modeling, design, and verification using conventional hardware description languages (HDLs), which are designed for level-based digital logic. Prior efforts have required complex Verilog support modules to enable Standard Delay Format (SDF) compatibility and have provided limited coverage of SFQ cell types. This work presents a Verilog-based modeling framework for SFQ gates that enables functional and timing verification while maintaining compatibility with Standard Delay Format (SDF) back annotation and is the first framework to support both synchronous and asynchronous SFQ gates. The proposed models are validated through device-level simulations, demonstrating correct functionality and timing constraint coverage. RTL simulation of mixed synchronous-asynchronous circuits further demonstrate the utility of the proposed framework.

As superconducting processors scale, understanding how physical layout shapes qubit interactions is essential for architectural reliability. Existing methods offer limited insight into how electromagnetic design choices translate into execution-level behavior. We present EPAR, an electromagnetic-to-architecture framework that predicts robustness early directly from physical design by reconstructing how design distortion modifies the effective Hamiltonian, reroutes mediated connectivity, and influences control-pulse response. Across all tested layouts, EPAR's structural scores show 100% agreement with two-qubit error trends yet reveal over 10X robustness differences among edges with identical calibrated error rates, going beyond conventional metrics to provide improved and actionable compiler guidance.

We present a formulation of the problem of finding the smallest T -Count circuit that implements a given unitary as a binary search over a sequence of continuous minimization problems, and demonstrate that these problems are numerically solvable in practice. We reproduce best-known results for synthesis of circuits with a small number of qubits, and push the bounds of the largest circuits that can be solved for in this way. Additionally, we show that circuit partitioning can be used to adapt this technique to be used to optimize the T -Count of circuits with large numbers of qubits by breaking the circuit into a series of smaller sub-circuits that can be optimized independently.

Magic and entanglement are two measures that are widely used to characterize quantum resources. We study the interplay between magic and entanglement in two-qubit systems, focusing on the two extremes: maximal magic and minimal magic for a given level of entanglement. We quantify magic by the Rényi entropy of order 2, $M_2$, and entanglement by the concurrence $Δ$. We find that the Pareto frontier of maximal magic $M_2^{(max)}(Δ)$ is composed of three separate segments, while the boundary of minimal magic $M_2^{(min)}(Δ)$ is a single continuous line. We derive simple analytical formulas for all these four cases, and explicitly parametrize all distinct quantum states of maximal or minimal magic at a given level of entanglement.

Discover how IonQ’s 64-qubit system systematically improves portfolio quality. See real-world benchmarks on S&P 500 data using the BF-DCQO algorithm and trapped-ion hardware.

Hybrid quantum-classical workflows combine quantum processing units (QPUs) with classical hardware to address computational tasks that are challenging or infeasible for conventional systems alone. Coordinating these heterogeneous resources at scale demands robust orchestration, reproducibility, and observability. Even in the presence of fault-tolerant quantum devices, quantum computing will continue to operate within a broader hybrid ecosystem, where classical infrastructure plays a central role in task scheduling, data movement, error mitigation, and large-scale workflow coordination. In this work, we present a cloud-native framework for managing hybrid quantum-HPC pipelines using Kubernetes, Argo Workflows, and Kueue. Our system unifies CPUs, GPUs, and QPUs under a single orchestration layer, enabling multi-stage workflows with dynamic, resource-aware scheduling. We demonstrate the framework with a proof-of-concept implementation of distributed quantum circuit cutting, showcasing execution across heterogeneous nodes and integration of classical and quantum tasks. This approach highlights the potential for scalable, reproducible, and flexible hybrid quantum-classical computing in cloud-native environments.

Quantum circuit initialisation is a key bottleneck in variational quantum algorithms (VQAs), strongly impacting optimisation stability and convergence. Recent work shows that large language models (LLMs) can synthesise high-quality variational circuit architectures, but their continuous parameter predictions are unreliable. Conversely, data-driven initialisation methods such as BEINIT improve trainability via problem-adaptive priors, yet assume fixed ansatz templates and ignore generative circuit structure. We propose BRIDG-Q (Barren-Plateau-Resilient Initialisation with Data-Aware LLM-Generated Quantum Circuits), a neuro-symbolic pipeline that bridges this gap by coupling LLM-generated circuit architectures with empirical-Bayes parameter initialisation. BRIDG-Q uses AgentQ to generate problem-conditioned circuit topologies, removes generated parameters, and injects data-informed parameter initialisations to mitigate barren plateau effects. Evaluations on graph optimisation benchmarks using residual energy gap and convergence metrics show improved optimisation robustness, indicating that data-driven initialisation remains effective even for LLM-generated circuits, with oracle per-instance selection achieving approximately a 10% reduction in final residual energy.

Machine vision, including object recognition and image reconstruction, is a central technology in many consumer devices and scientific instruments. The design of machine-vision systems has been revolutionized by the adoption of end-to-end optimization, in which the optical front end and the post-processing back end are jointly optimized. However, while machine vision currently works extremely well in moderate-light or bright-light situations -- where a camera may detect thousands of photons per pixel and billions of photons per frame -- it is far more challenging in very low-light situations. We introduce photon-aware neuromorphic sensing (PANS), an approach for end-to-end optimization in highly photon-starved scenarios. The training incorporates knowledge of the low photon budget and the stochastic nature of light detection when the average number of photons per pixel is near or less than 1. We report a proof-of-principle experimental demonstration in which we performed low-light image classification using PANS, achieving 73% (82%) accuracy on FashionMNIST with an average of only 4.9 (17) detected photons in total per inference, and 86% (97%) on MNIST with 8.6 (29) detected photons -- orders of magnitude more photon-efficient than conventional approaches. We also report simulation studies showing how PANS could be applied to other classification, event-detection, and image-reconstruction tasks. By taking into account the statistics of measurement results for non-classical states or alternative sensing hardware, PANS could in principle be adapted to enable high-accuracy results in quantum and other photon-starved setups.

To get the most out of today’s noisy quantum computers, quantum computational experiments commonly utilize quantum error mitigation (QEM) techniques. These methods include discarding known noisy results (post selection), modifying underlying pulse sequences, amplifying noise within a quantum circuit, and many more. QEM does not offer fault tolerant or error-free means of computation but can generally be used to improve the quality of a result, for example increasing signal from noise via repeated observations. In this blog post, you will learn how Amazon Braket’s program sets can be used for error mitigation with toolkits such as Mitiq to improve quantum computational accuracy while substantially reducing task-related costs. Using program sets, we performed a 30-qubit error mitigation experiment on Rigetti’s Ankaa-3 processor that achieved more than 12x reduction in error with an 86x reduction in task costs. Here, we highlight some common error mitigation techniques, detailed in new notebooks in the Amazon Braket Examples repository . Error mitigation and program sets Amazon Braket’s program sets are well suited for common error mitigation tasks on today’s quantum devices, as many variations of a single quantum circuit are required. With program sets, you can submit multiple circuits in a single task, which speeds up execution times and decreases the total cost for task submissions. Figure 1. Depicts how an error mitigated workflow can generate multiple copies – here from an observable, a set of noise amplified circuits for use in zero-noise extrapolation, and variations from Pauli twirling. These can all be executed in a single program set on Amazon Braket. In addition to increasing the number of circuits, error mitigation has a theoretical worst-case exponential scaling in the number of additional shots, leading to increased cost and execution time. The examples below and in the Example Notebooks , provide resources to help understand these overheads while using p

Quantum error correcting codes (QECC) are essential for constructing large-scale quantum computers that deliver faithful results. As strong competitors to the conventional surface code, quantum low-density parity-check (qLDPC) codes are emerging rapidly: they offer high encoding rates while maintaining reasonable physical-qubit connectivity requirements. Despite the existence of numerous code constructions, a notable gap persists between these designs -- some of which remain purely theoretical -- and their circuit-level deployment. In this work, we propose Auto-Stabilizer-Check (ASC), a universal compilation framework that generates depth-optimal syndrome extraction circuits for arbitrary qLDPC codes. ASC leverages the sparsity of parity-check matrices and exploits the commutativity of X and Z stabilizer measurement subroutines to search for optimal compilation schemes. By iteratively invoking an SMT solver, ASC returns a depth-optimal solution if a satisfying assignment is found, and a near-optimal solution in cases of solver timeouts. Notably, ASC provides the first definitive answer to one of IBM's open problems: for all instances of bivariate bicycle (BB) code reported in their work, our compiler certifies that no depth-6 syndrome extraction circuit exists. Furthermore, by integrating ASC with an end-to-end evaluation framework -- one that assesses different compilation settings under a circuit-level noise model -- ASC reduces circuit depth by approximately 50% and achieves an average 7x-8x suppression of the logical error rate for general qLDPC codes, compared with as-soon-as-possible (ASAP) and coloration-based scheduling. ASC thus substantially reduces manual design overhead and demonstrates its strong potential to serve as a key component in accelerating hardware deployment of qLDPC codes.

Classical supply chain risk models treat node failures as statistically independent events, systematically underestimating cascade probabilities when supplier dependencies are strongly correlated. At n=40 nodes, the full correlated failure distribution requires O(2^n) classical samples, a regime where exact simulation demands 17.6 TB of memory and over 369,000 hours of computation on a standard workstation. We present QR-SPPS (Quantum-Native Retail Shock Propagation and Policy Stress Simulator), a three-algorithm quantum pipeline implemented using the Qiskit framework with the Aer statevector_simulator backend. First, a 40-node, 4-tier retail supply network is encoded as a 40-qubit Ising Hamiltonian using OpenFermion QubitOperator, where ZZ coupling terms encode correlated cascade probabilities structurally absent from classical Monte Carlo. Second, a hardware-efficient VQE circuit finds the ground-state stress distribution with zero error, detecting entangled cascade failures in 14/40 nodes with max|ΔP|=0.637 versus classical Monte Carlo. Third, we introduce the first application of ADAPT-VQE gradient screening to counterfactual macroeconomic policy evaluation: six crisis interventions are ranked in O(1) Qiskit operator evaluations per policy, a 287x speedup over sequential VQE re-optimisation. Fourth, Density-of-States QPE (DOS-QPE) reconstructs the full eigenspectrum via 32-step Trotter evolution and introduces a novel mapping of the Boltzmann catastrophe probability P_cat(T) to VIX-equivalent market volatility temperature, enabling direct integration into regulatory Value-at-Risk frameworks. Qiskit Aer scaling benchmarks confirm exponential classical intractability at 40 qubits.

The scalability of quantum computing in supporting sophisticated algorithms critically depends not only on qubit quality and error handling, but also on the efficiency of classical control, constrained by the cryogenic control bandwidth and energy budget. In this work, we address this challenge by investigating the algorithmic complexity of quantum circuits at the instruction set architecture (ISA) level. We introduce an energy-efficient quantum instruction set architecture (EQISA) that synthesizes quantum circuits in a discrete Solovay-Kitaev basis of fixed depth and encodes instruction streams using a sparse dictionary learned from decomposing a set of Haar-random unitaries, followed by entropy-optimal Huffman coding and an additional lossless bzip2 compression stage. This approach is evaluated on benchmark quantum circuits demonstrating over 60% compression of quantum instruction streams across system sizes, enabling proportional reductions in classical control energy and communication overhead without loss of computational fidelity. Beyond compression, EQISA facilitates the discovery of higher-level composable abstractions in quantum circuits and provides estimates of quantum algorithmic complexity. These findings position EQISA as an impactful direction for improving the energy efficiency and scalability of quantum control architectures.

In this work, we review quantum approaches to combinatorial optimization, with the aim of bridging theoretical developments and industrial relevance. We first survey the main families of quantum algorithms, including Quantum Annealing, the Quantum Approximate Optimization Algorithm (QAOA), Quantum Reinforcement Learning (QRL), and Quantum Generative Modeling (QGM). We then examine the problem classes where quantum technologies currently show evidence of quantum advantage, drawing on established benchmarking initiatives such as QOBLIB, QUARK, QASMBench, and QED-C. These problem classes are subsequently mapped to representative industrial domains, including logistics, finance, and telecommunications. Our analysis indicates that quantum annealing currently exhibits the highest level of operational maturity, while QAOA shows promising potential on NISQ-era hardware. In contrast, QRL and QGM emerge as longer-term research directions with significant potential for future industrial impact.

Aerodynamic drag reduction on highways through vehicle platooning is a well-known concept, but it has not yet seen systematic uptake, arguably because of significant technological and legislative obstacles. As a low-tech entry point to real multi-vehicle platooning, "Windbreaking-as-a-Service" (WaaS) was introduced recently. Here we use a QUBO formulation to study classical metaheuristics such as simulated annealing and tabu search, together with emerging quantum heuristics including quantum annealing and variants of the Quantum Approximate Optimization Algorithm (QAOA). These heuristic solvers do not guarantee optimality, but they traverse the same higher-order landscape using polynomial memory. They can also be parallelized aggressively, and efficient classical post-processing can be used in hybrid workflows to return only valid schedules. This paper therefore positions QUBO as a common language that allows heterogeneous classical, quantum, and hybrid solvers to address the optimization of highway platooning.

As VLSI designs grow in complexity, partitioning is widely adopted to accelerate physical design through parallel computing. However, traditional hypergraph partitioning methods often degrade in performance when applied to 2D layouts due to spatial constraints. For routers with post-placement locations, a spatial-aware partitioning method fully utilizing placement data is preferable. Existing works can only consider soft spatial constraints, leading to a scattered distribution in one partition. We propose SAAP, an analytic partitioning algorithm enforcing hard spatial constraints while efficiently minimizing cut sizes. It includes analytic boundary modeling with regularity-guided simulated annealing and region embedding. Given placed netlists, it generates timing-friendly k-way spatially continuous partitions for parallel routing. Experiments show that it can quickly provide several to dozens of times smaller spatial cut sizes than previous state-of-the-art, with better spatial continuity.

With current noisy quantum hardware, every quantum circuit evaluation is precious. Variational quantum algorithms like the Variational Quantum Eigensolver (VQE) require repeated estimation of expectation values of quantum observables—each requiring multiple shots , or measurements of quantum states. On today’s hardware, these shots represent a finite resource that needs to be managed carefully. Efficient shot allocation therefore improves algorithm performance and reduces quantum runtime. This post explores how shot allocation techniques can reduce errors in quantum expectation value estimation, without increasing the total shot cost. To help users understand and experiment with these advanced strategies, we released an educational implementation of an adaptive shot allocation algorithm in the Amazon Braket Algorithms Library , based on the paper “Adaptive Estimation of Quantum Observables” (Shlosberg et al., 2023). As a starting point, we published two new interactive notebooks in the Braket Algorithms Library: Intro to Shot Allocation : A hands-on introduction to the shot allocation problem and its impact on expectation value estimation. Adaptive Shot Allocation : A step-by-step walkthrough of the algorithm and how to use it with observables in Braket. Why shot allocation matters in quantum algorithms Iterative estimation of expectation values is a common pattern in near-term quantum algorithms. In VQE, for example, the energy of a molecular Hamiltonian is computed as the weighted sum of expectation values of Pauli terms. Each term requires estimation from repeated measurements and with limited quantum runtime available, how we allocate these measurements—or shots —impacts the estimator error. Comparing naive and optimal allocation A naive approach assigns the same number of shots to each term. But this ignores key differences in variance and contribution of each term to the result. Terms with larger weights or higher variance contribute more to the overall estima