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arXiv:2307.09667 · Physical Review A

Information-theoretic approach to readout-error mitigation for quantum computers

H. Chau Nguyen

Published Nov 17, 2023• 2 citations
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Abstract

We show that the method of iterative Bayesian unfolding for mitigating readout errors in quantum computers can be derived from an information theoretic analysis. This inspires more flexible applications of this error-mitigation scheme. In particular, we distinguish between structural mitigation and unstructural mitigation. Structural mitigation addresses nearly deterministic quantum computation, where the computer is expected to output a single- or few-outcome bit strings. It is shown that the readout errors alone can be corrected by few repetitions of the computation. In contrast, unstructural mitigation is designed for quantum simulation, where the computer outputs bit strings broadly distributed. In this case, one is interested in mitigating certain observables of interest. As most observables of interest are dependent on few bits and not the whole bit string, it is sufficient to mitigate the marginal distributions over these dependent bits. As long as the cross talk of readout errors can be ignored, it is shown that the iterative Bayesian unfolding applied locally for these marginal distributions gives similar results as mitigation using least squared errors. We illustrate our analysis using the data of the preparation of the Greenberger-Horne-Zeilinger state in a 127-qubit quantum computer.

DOI
10.1103/physreva.108.052419

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Measurement error mitigation (MEM) techniques are postprocessing strategies to counteract systematic read-out errors on quantum computers (QC). Currently used MEM strategies face a tradeoff: methods that scale well with the number of qubits return negative probabilities, while those that guarantee a valid probability distribution are not scalable. Here, we present a scheme that addresses both of these issues. In particular, we present a scalable implementation of iterative Bayesian unfolding, a standard mitigation technique used in high-energy physics experiments. We demonstrate our method by mitigating QC data from experimental preparation of Greenberger-Horne-Zeilinger (GHZ) states up to 127 qubits and implementation of the Bernstein-Vazirani algorithm on up to 26 qubits.
Abstract In the current era of noisy intermediate-scale quantum computers, noisy qubits can result in biased results for early quantum algorithm applications. This is a significant challenge for interpreting results from quantum computer simulations for quantum chemistry, nuclear physics, high energy physics (HEP), and other emerging scientific applications. An important class of qubit errors are readout errors. The most basic method to correct readout errors is matrix inversion, using a response matrix built from simple operations to probe the rate of transitions from known initial quantum states to readout outcomes. One challenge with inverting matrices with large off-diagonal components is that the results are sensitive to statistical fluctuations. This challenge is familiar to HEP, where prior-independent regularized matrix inversion techniques (“unfolding”) have been developed for years to correct for acceptance and detector effects, when performing differential cross section measurements. We study one such method, known as iterative Bayesian unfolding, as a potential tool for correcting readout errors from universal gate-based quantum computers. This method is shown to avoid pathologies from commonly used matrix inversion and least squares methods.
Measurement errors are a significant obstacle to achieving scalable quantum computation. To counteract systematic readout errors, researchers have developed postprocessing techniques known as measurement error mitigation methods. However, these methods face a tradeoff between scalability and returning nonnegative probabilities. In this paper, we present a solution to overcome this challenge. Our approach focuses on iterative Bayesian unfolding, a standard mitigation technique used in high-energy physics experiments, and implements it in a scalable way. We demonstrate our method on experimental Greenberger-Horne-Zeilinger state preparation on up to 127 qubits and on the Bernstein-Vazirani algorithm on up to 26 qubits. Compared to state-of-the-art methods (such as M3), our implementation guarantees valid probability distributions, returns comparable or better-mitigated results, and does so without a noticeable time and memory overhead. Published by the American Physical Society 2024
Readout errors on near-term quantum computers can introduce significant error to the empirical probability distribution sampled from the output of a quantum circuit. These errors can be mitigated by classical postprocessing given the access of an experimental response matrix that describes the error associated with the measurement of each computational basis state. However, the resources required to characterize a complete response matrix and to compute the corrected probability distribution scale exponentially with the number of qubits, nnn. In this work, we modify standard matrix inversion techniques using perturbative approximations with significantly reduced complexity and bounded error when the likelihood of high-order bit-flip events is strongly suppressed. Given a characteristic error rate qqq, we discuss a method to recover the probability of the all-zeros bit string p0{p}_{0}p0​ by sampling only a small subspace of the response matrix before inverting readout error, resulting in a relative speedup of poly[2n/(nw)]\text{poly}[{2}^{n}/(\begin{array}{c}n\\ w\end{array})]poly[2n/(nw​)], which we motivate using a simplified error model for which the approximation incurs only O(qw)O({q}^{w})O(qw) error for some integer www. We then provide a generalized technique to efficiently recover full output distributions with O(qw)O({q}^{w})O(qw) error in the perturbative limit. These approximate techniques for readout-error correction may greatly accelerate near-term quantum computing applications.
In Phys. Rev. A 108, L060402 (2023), we introduced a Bayesian measurement error mitigation algorithm, which leveraged complete information from the readout signal, and validated the protocol on a quantum device with five superconducting qubits. Here, we present an improved algorithm's implementation, tailored for multiqubit experiments on near-term superconducting qubit quantum devices. In particular, we provide a detailed algorithm workflow, from calibrating the detector response functions to the postprocessing of measurement outcomes, offering a computationally efficient solution for the output size typical of current quantum computing devices. We show how the numerical representation of the noise function affects the performance of the error mitigation algorithm and test the convergence criteria. We benchmark our protocol on actual quantum computers with superconducting qubits, where the readout signal encodes the measurement information as unprocessed analog data before qubit state assignment. Finally, we compare the performance of our algorithm against other measurement error mitigation methods, such as iterative Bayesian unfolding and the Mthree method, and show how our method can be integrated on top of other readout error mitigation protocols.