arXiv subjects

Adrian Harkness

Publications and source records attributed to Adrian Harkness.

7 recordsLinked to original sources

arXiv2026

An analysis of iterative refinement for quantum linear system solvers

We present and analyze an iterative refinement (IR) framework for improving the precision dependence of algorithms that combine a quantum linear system algorithm (QLSA) with quantum state tomography. Existing QLSAs achieve polylogarithmic dependence on the inverse error tolerance to prepare a quantum state encoding the solution, but extracting a classical description of such a state via tomography typically introduces a polynomial dependence on the target precision. To retain polylogarithmic dependence in the inverse error tolerance throughout the entire process, we develop an IR scheme that solves a sequence of related linear systems to progressively refine the solution while requiring only fixed-precision quantum subroutines, finally obtaining a classical description of a high-precision solution. We analyze the proposed framework under three input models: quantum-read/classical-write RAM (QRAM), linear combinations of unitaries (LCU), and sparse-access oracles. We evaluate the proposed scheme through numerical experiments on both quantum simulators and real quantum hardware. The results demonstrate that iterative refinement efficiently improves the precision of the solution and exhibits robustness to hardware noise.

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arXiv2026

FTPrimitiveBench: A Benchmark Suite For Logical Computation Under Hardware-Motivated and Biased Noise Models

Fault-tolerant quantum computing requires understanding how error-correcting codes perform on diverse physical hardware. This is typically assessed via noisy stabilizer simulation of logical circuits at HPC scale, combined with a noise model that yields a logical error rate for the relevant code distances and depths. The uniform depolarizing model is the standard baseline, but its homogeneous assumptions fail to capture the heterogeneity, asymmetries, and correlations of real devices, where Pauli, measurement, and spatio-temporal errors are not weakly coupled. Yet these same structured features create opportunities for joint code-hardware co-design, motivating noise models that more faithfully reflect target hardware while remaining tractable to simulate. We introduce FTPrimitiveBench, a systematic benchmarking approach for studying how logical primitives interact with hardware-motivated noise. It supports both custom specifications and representative structured noise families: Pauli bias, measurement bias, and spatial or spatio-temporal non-uniformity -- together with generators for core surface-code Clifford primitives: logical memory, lattice surgery, transversal logical Hadamard, and the logical phase gate via lattice surgery. We find that structured noise affects these primitives in qualitatively distinct ways, with outcomes shaped by the interplay between noise model, primitive, and decoder choice. These results extend memory benchmarks to active logical computation, where the interaction between noise structure and primitive implementation matters. By standardizing the link between noise-model specification and primitive construction, FTPrimitiveBench enables reproducible comparative studies of QEC protocols and decoders, supporting hardware-aware co-design of fault-tolerant architectures. Code: https://github.com/ShuwenKan/FTPrimitiveBench.

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arXiv2026

Calibration-Conditioned FiLM Decoders for Low-Latency Decoding of Quantum Error Correction Evaluated on IBM Repetition-Code Experiments

Real-time decoding of quantum error correction (QEC) is essential for enabling fault-tolerant quantum computation. A practical decoder must operate with high accuracy at low latency, while remaining robust to spatial and temporal variations in hardware noise. We introduce a hardware-conditioned neural decoder framework designed to exploit the natural separation of timescales in superconducting processors, where calibration drifts occur over hours while error correction requires microsecond-scale responses. By processing calibration data through a graph-based encoder and conditioning a lightweight convolutional backbone via feature-wise linear modulation (FiLM), we decouple the heavy processing of device statistics from the low-latency syndrome decoding. We evaluate this approach using the 1D repetition code as a testbed on IBM Fez, Kingston, and Pittsburgh processors, collecting over 2.7 million experimental shots spanning distances up to d = 11. We demonstrate that a single trained model generalizes to unseen qubit chains and new calibration data acquired days later without retraining. On these unseen experiments, the FiLM-conditioned decoder achieves up to an 11.1x reduction in logical error rate relative to modified minimum-weight perfect matching. We observe that by employing a network architecture that exploits the highly asynchronous nature of system calibration and decoding, hardware-conditioned neural decoding demonstrates promising, adaptive performance with negligible latency overhead relative to unconditioned baselines.

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arXiv2026

FTCircuitBench: A Benchmark Suite for Fault-Tolerant Quantum Compilation and Architecture

Realizing large-scale quantum advantage is expected to require quantum error correction (QEC), making the compilation and optimization of logical operations a critical area of research. Logical computation imposes distinct constraints and operational paradigms that differ from those of the Noisy Intermediate-Scale Quantum (NISQ) regime, motivating the continued evolution of compilation tools. Given the complexity of this emerging stack, where factors such as gate decomposition precision and computational models must be co-designed, standardized benchmarks and toolkits are valuable for evaluating progress. To support this need, we introduce FTCircuitBench, which serves as: (1) a benchmark suite of impactful quantum algorithms, featuring pre-compiled instances in both Clifford+T and Pauli Based Computation models; (2) a modular end-to-end pipeline allowing users to compile and decompose algorithms for various fault-tolerant architectures, supporting both prebuilt and custom optimization passes; and (3) a toolkit for evaluating the impact of algorithms and optimization across the full compilation stack, providing detailed numerical analysis at each stage. FTCircuitBench is fully open-sourced and maintained on Github.

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arXiv2025

Quantum Interior Point Methods: A Review of Developments and An Optimally Scaling Framework

The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior point methods (IPMs). Despite their favorable polynomial-time convergence, conventional IPMs often suffer from high per-iteration computational costs, especially for dense problem instances. Recent advances in quantum computing, particularly quantum linear system solvers, offer promising avenues to accelerate the most computationally intensive steps of IPMs. However, practical challenges such as quantum error, hardware noise, and sensitivity to poorly conditioned systems remain significant obstacles. In response, a series of Quantum IPMs (QIPMs) has been developed to address these challenges, incorporating techniques such as feasibility maintenance, iterative refinement, and preconditioning. In this work, we review this line of research with a focus on our recent contributions, including an almost-exact QIPM framework. This hybrid quantum-classical approach constructs and solves the Newton system entirely on a quantum computer, while performing solution updates classically. Crucially, all matrix-vector operations are executed on quantum hardware, enabling the method to achieve an optimal worst-case scalability w.r.t dimension, surpassing the scalability of existing classical and quantum IPMs.

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arXiv2025

Characterizing QUBO Reformulations of the Max-k-Cut Problem for Quantum Computing

Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a quadratic unconstrained binary optimization (QUBO) problem. The solution of the QUBO reformulation can then be addressed using adiabatic quantum computing devices or appropriate quantum computing algorithms on gate-based quantum computing devices. In general, QUBO reformulations of combinatorial problems can be readily obtained by properly penalizing the violation of the problem's constraints in the original problem's objective. However, characterizing tight (i.e., minimal but sufficient) penalty coefficients for this purpose is important and non-trivial for enabling the solution of the resulting QUBO in current and near-term quantum computing devices. Along these lines, we present closed-form characterizations of tight penalty coefficients for two distinct QUBO reformulations of the max $k$-cut problem whose values depend on the (weighted) degree of the vertices of the graph defining the problem. These findings contribute to the ongoing effort to make quantum computing a viable tool for solving combinatorial problems at scale. We support our theoretical results with illustrative examples and simple numerical results.

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arXiv2024

Security of Partially Corrupted Repeater Chains

Quantum Key Distribution allows two parties to establish a secret key that is secure against computationally unbounded adversaries. To extend the distance between parties, quantum networks, and in particular repeater chains, are vital. Typically, security in such scenarios assumes the absolute worst case: namely, an adversary has complete control over all repeaters and fiber links in a network and is able to replace them with perfect devices, thus allowing her to hide her attack within the expected natural noise. In a large-scale network, however, such a powerful attack may be infeasible. In this paper, we analyze the case where the adversary can only corrupt a contiguous subset of a repeater chain connecting Alice and Bob, while some portion of the network near Alice and Bob may be considered safe from attack (though still noisy). We derive a rigorous finite key proof of security assuming this attack model and show that improved performance and noise tolerances are possible.

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