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arXiv:2204.01529 · Entropy

Characterizing the Reproducibility of Noisy Quantum Circuits

Samudra Dasgupta, Travis S. Humble

Published Feb 5, 2022• 31 citations
arXivHTMLPDF

Abstract

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.

DOI
10.3390/e24020244

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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.
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.
Reproducibility is important for validating the performance of applications in quantum computing as a measure of consistency in computation. Current noisy, intermediate-scale devices quantum (NISQ) devices are strongly affected by intrinsic noise that leads to a variety of computational error mechanisms. Here we assess reproducibility of NISQ computing by focusing on a specific simple error mechanism that arises during noisy readout. Using an asymmetric channel for binary readout, we develop an analytic bound on the Hellinger distance between computational outputs for different readout parameters. We validate this model using characterization and testing of the IBM toronto device, which displays a range of readout parameters. We find that to ensure reproducibility, one must avoid using register elements characterized by fidelity asymmetry exceeding a threshold.
Effective methods for characterizing the noise in quantum computing devices are essential for programming and debugging circuit performance. Existing approaches vary in the information obtained as well as the amount of quantum and classical resources required, with more information generally requiring more resources. Here we benchmark the characterization methods of gate set tomography, Pauli channel noise reconstruction, and empirical direct characterization for developing models that describe noisy quantum circuit performance on a 27-qubit superconducting transmon device. We evaluate these models by comparing the accuracy of noisy circuit simulations with the corresponding experimental observations. We find that the agreement of noise model to experiment does not correlate with the information gained by characterization and that the underlying circuit strongly influences the best choice of characterization approach. Empirical direct characterization scales best of the methods we tested and produced the most accurate characterizations across our benchmarks.
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.
Noisy intermediate-scale quantum (NISQ) devices offer unique platforms to test and evaluate the behavior of quantum computing. However, validating circuits on NISQ devices is difficult due to fluctuations in the underlying noise sources and other nonreproducible behaviors that generate computational errors. Here we present a test-driven approach that decomposes a noisy, application-specific circuit into a series of bootstrapped experiments on a NISQ device. By characterizing individual subcircuits, we generate a composite noise model for the original quantum circuit. We demonstrate this approach to model applications of Greenberger-Horne-Zeilinger(GHZ)-state preparation and the Bernstein-Vazirani algorithm on a family of superconducting transmon devices. We measure the model accuracy using the total variation distance between predicted and experimental results, and we demonstrate that the composite model works well across multiple circuit instances. Our approach is shown to be computationally efficient and offers a trade-off in model complexity that can be tailored to the desired predictive accuracy.
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.