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arXiv:2208.07219 · Quantum Communications and Quantum Imaging

Assessing the stability of noisy quantum computation

Samudra Dasgupta, Travis S. Humble

Published Oct 4, 2022• 14 citations
arXivHTMLPDF

Abstract

Quantum computation has made considerable progress in the last decade with multiple emerging technologies providing proof-of-principle experimental demonstrations of such calculations. However, these experimental demonstrations of quantum computation face technical challenges due to the noise and errors that arise from imperfect implementation of the technology. Here, we frame the concepts of computational accuracy, result reproducibility, device reliability and program stability in the context of quantum computation. We provide intuitive definitions for these concepts in the context of quantum computation that lead to operationally meaningful bounds on program output. Our assessment highlights the continuing need for statistical analyses of quantum computing program to increase our confidence in the burgeoning field of quantum information science.

DOI
10.1117/12.2631809

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Quantum computation has made considerable progress in the last decade with multiple emerging technologies providing proof-of-principle experimental demonstrations of such calculations. However, these experimental demonstrations of quantum computation face technical challenges due to the noise and errors that arise from imperfect implementation of the technology. Here, we frame the concepts of computational accuracy, result reproducibility, device reliability and program stability in the context of quantum computation. We provide intuitive definitions for these concepts in the context of quantum computation that lead to operationally meaningful bounds on program output. Our assessment highlights the continuing need for statistical analyses of quantum computing program to increase our confidence in the burgeoning field of quantum information science.
Noisy intermediate-scale quantum (NISQ) devices are valuable platforms for testing the tenets of quantum computing, but these devices are susceptible to errors arising from de-coherence, leakage, cross-talk, and other sources of noise. This raises concerns regarding the stability of results when using NISQ devices since strategies for mitigating errors generally require well-characterized and stationary error models. Here, we quantify the reliability of NISQ devices by assessing the necessary conditions for generating stable results within a given tolerance. We use similarity metrics derived from device characterization data to derive and validate bounds on the stability of a 5-qubit implementation of the Bernstein-Vazirani algorithm. Simulation experiments conducted with noise data from IBM washington, spanning January 2022 to April 2023, revealed that the reliability metric fluctuated between 41% and 92%. This variation significantly surpasses the maximum allowable threshold of 2.2% needed for stable outcomes. Consequently, the device proved unreliable for consistently reproducing the statistical mean in the context of the Bernstein-Vazirani circuit.
Stable quantum computation requires noisy results to remain bounded even in the presence of noise fluctuations. Yet non-stationary noise processes lead to drift in the varying characteristics of a quantum device that can greatly influence the circuit outcomes. Here we address how temporal and spatial variations in noise relate device reliability to quantum computing stability. First, our approach quantifies the differences in statistical distributions of characterization metrics collected at different times and locations using Hellinger distance. We then validate an analytical bound that relates this distance directly to the stability of a computed expectation value. Our demonstration uses numerical simulations with models informed by the washington superconducting transmon device. We find that the stability metric is consistently bounded from above by the corresponding Hellinger distance, which can be cast as a specified tolerance level. These results underscore the significance of reliable quantum computing devices and the impact for stable quantum computation.
The ability of a quantum computer to reproduce or replicate the results of a quantum circuit is a key concern for verifying and validating applications of quantum computing. Statistical variations in circuit outcomes that arise from ill-characterized fluctuations in device noise may lead to computational errors and irreproducible results. While device characterization offers a direct assessment of noise, an outstanding concern is how such metrics bound the reproducibility of a given quantum circuit. Here, we first directly assess the reproducibility of a noisy quantum circuit, in terms of the Hellinger distance between the computational results, and then we show that device characterization offers an analytic bound on the observed variability. We validate the method using an ensemble of single qubit test circuits, executed on a superconducting transmon processor with well-characterized readout and gate error rates. The resulting description for circuit reproducibility, in terms of a composite device parameter, is confirmed to define an upper bound on the observed Hellinger distance, across the variable test circuits. This predictive correlation between circuit outcomes and device characterization offers an efficient method for assessing the reproducibility of noisy quantum circuits.
This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for understanding how noise and intrinsic randomness shape quantum computational outcomes in the language of mathematics. By grounding quantum computation in statistical inference, we highlight how mathematical tools such as probabilistic modeling, stochastic analysis, Bayesian inference, and sensitivity analysis, can directly address error propagation and reliability challenges in today's quantum devices. We also connect these methods to key scientific priorities in the field, including scalable uncertainty-aware algorithms and characterization of correlated errors. The purpose is to narrow the conceptual divide between applied mathematics, scientific computing and quantum information sciences, demonstrating how mathematically rooted UQ methodologies can guide validation, error mitigation, and principled algorithm design for emerging quantum technologies, in order to address challenges and opportunities present in modern-day quantum high performance and fault-tolerant quantum computing paradigms.
Noisy, intermediate-scale quantum (NISQ) computing devices offer opportunities to test the principles of quantum computing but are prone to errors arising from various sources of noise. Fluctuations in the noise itself lead to unstable devices that undermine the reproducibility of NISQ results. Here we characterize the reliability of NISQ devices by quantifying the stability of essential performance metrics. Using the Hellinger distance, we quantify the similarity between experimental characterizations of several NISQ devices by comparing gate fidelities, duty cycles, and register addressability across temporal and spatial scales. Our observations collected over 22 months reveal large fluctuations in each metric that underscore the limited scales on which current NISQ devices may be considered reliable.
The current stage of quantum computing development is defined by Noisy Intermediate-Scale Quantum (NISQ) devices, which operate with a moderate number of qubits that are inherently susceptible to noise and decoherence. Despite the absence of full error correction, NISQ systems have demonstrated the ability to perform computational tasks that challenge classical simulation under certain conditions. This paper explores the concept of quantum advantage in the NISQ era by analysing prominent algorithmic approaches, benchmarking methodologies, and the practical constraints imposed by contemporary hardware. Hybrid quantum–classical algorithms, sampling-based experiments, and performance metrics are examined to assess the extent to which near-term quantum devices can outperform classical systems. The study finds that while progress toward quantum advantage is evident, significant technical and algorithmic limitations prevent its widespread realization. The paper concludes by identifying key research directions required to bridge the gap between experimental demonstrations and practical quantum computing applications.