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arXiv:2010.07496 · Physical Review A

Readout rebalancing for near-term quantum computers

Rebecca Hicks, C. Bauer, Benjamin Philip Nachman

Published Feb 5, 2021• 30 citations
arXivHTMLPDF

Abstract

Readout errors are a significant source of noise for near-term intermediate-scale quantum computers. Mismeasuring a qubit as $|1\ensuremath{\rangle}$ when it should be $|0\ensuremath{\rangle}$ occurs much less often than mismeasuring a qubit as $|0\ensuremath{\rangle}$ when it should have been $|1\ensuremath{\rangle}$. We make the simple observation that one can improve the readout fidelity of quantum computers by applying targeted $X$ gates prior to performing a measurement. These $X$ gates are placed so that the expected number of qubits in the $|1\ensuremath{\rangle}$ state is minimized. Classical postprocessing can undo the effect of the $X$ gates so that the expectation value of any observable is unchanged. This protocol is designed to have no effect when readout errors are symmetric. We show that the statistical uncertainty following readout error corrections is smaller when using readout rebalancing. The statistical advantage is circuit and computer dependent and is demonstrated for the $W$ state, a Grover search, and for a Gaussian state. The benefit in statistical precision is most pronounced (and nearly a factor of 2 in some cases) when states with many qubits in the excited state have high probability.

DOI
10.1103/physreva.103.022407

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Readout errors are a significant source of noise for near-term intermediate-scale quantum computers. Mismeasuring a qubit as ∣1\ensuremath⟩|1\ensuremath{\rangle}∣1\ensuremath⟩ when it should be ∣0\ensuremath⟩|0\ensuremath{\rangle}∣0\ensuremath⟩ occurs much less often than mismeasuring a qubit as ∣0\ensuremath⟩|0\ensuremath{\rangle}∣0\ensuremath⟩ when it should have been ∣1\ensuremath⟩|1\ensuremath{\rangle}∣1\ensuremath⟩. We make the simple observation that one can improve the readout fidelity of quantum computers by applying targeted XXX gates prior to performing a measurement. These XXX gates are placed so that the expected number of qubits in the ∣1\ensuremath⟩|1\ensuremath{\rangle}∣1\ensuremath⟩ state is minimized. Classical postprocessing can undo the effect of the XXX gates so that the expectation value of any observable is unchanged. This protocol is designed to have no effect when readout errors are symmetric. We show that the statistical uncertainty following readout error corrections is smaller when using readout rebalancing. The statistical advantage is circuit and computer dependent and is demonstrated for the WWW state, a Grover search, and for a Gaussian state. The benefit in statistical precision is most pronounced (and nearly a factor of 2 in some cases) when states with many qubits in the excited state have high probability.
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.
The readout error on near-term quantum devices is one of the dominant noise factors, which can be mitigated by classical postprocessing called quantum readout error mitigation (QREM). The standard QREM applies the inverse of noise calibration matrix to the outcome probability distribution using exponential computational resources to the number of measured qubits. This becomes infeasible for the current quantum devices with tens of qubits or more. Here we propose two efficient QREM methods finishing in O(ns2)O(n{s}^{2})O(ns2) time for probability distributions of nnn qubits and sss shots, which mainly aim at mitigating sparse probability distributions such that only a few states are dominant. We compare the proposed methods with several recent QREM methods in the following three cases: expectation values of the GHZ state, its fidelities, and the estimation error of maximum likelihood amplitude estimation (MLAE) algorithm with a modified Grover iterator. The two cases of the GHZ state are on real IBM quantum devices, while the third is with numerical simulation. Using the proposed method, the mitigation of the 65-qubit GHZ state takes only a few seconds, and we witness the fidelity of the 29-qubit GHZ state exceeding 0.5. The proposed methods also succeed in reducing the estimation error in the MLAE algorithm, outperforming the results by other QREM methods in general.
Reading a qubit is a fundamental operation in quantum computing. It translates quantum information into classical information enabling subsequent classification to assign the qubit states '0' or '1'. Unfortunately, qubit readout is one of the most error-prone and slowest operations on a superconducting quantum processor. On state-of-the-art superconducting quantum processors, readout errors can range from 1--10%. These errors occur for various reasons - crosstalk, spontaneous state transitions, and excitation caused by the readout pulse. The error-prone nature of readout has resulted in significant research to design better discriminators to achieve higher qubit-readout accuracies. High readout accuracy is essential for enabling high fidelity for near-term noisy quantum computers and error-corrected quantum computers of the future.
Mitigating errors is a significant challenge for near-term quantum computers. One of the most important sources of errors is related to the readout of the quantum state into a classical bit stream. A variety of techniques have been proposed to mitigate these errors with post-hoc corrections. We propose a complementary scheme to actively reduce readout errors on a shot-by-shot basis by encoding single qubits, immediately prior to readout, into multiqubit states. The computational resources of our technique are independent of the circuit depth and are compatible with the error rates and connectivity of many current devices. We analyze the potential of our approach using two types of error-correcting codes, and, as a proof of principle, we demonstrate an 80% improvement in readout error on the IBMQ Mumbai quantum computer.
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.
The field of quantum technologies has experienced explosive growth in the past decade. As hardware capabilities have advanced, quantum computing has exhibited a scaling trend analogous to Moore's law, often referred to as Rose's law, where the number of coherently controlled qubits roughly doubles every two years. Associated with such rapid growth is an equally growing need for benchmarking tools and error handling. While advancements in quantum hardware and software have mainly concentrated on enhancing gate fidelity and qubit connectivity, the progress in addressing readout errors has been relatively limited during the same period. This thesis tries to close this gap by advancing and developing new tools for information extraction in quantum systems. We do this in two different ways: In Part II, we focus on mitigating the effect of general readout errors in quantum systems. We developed a comprehensive protocol for readout-error-mitigated state tomography (REMST) and implemented it on a superconducting qubit system. The REMST protocol was designed to mitigate not only classical readout errors but also more challenging coherent and correlated readout errors. The protocol uses only a deterministic application of single-qubit readout, making it one of the most experimentally friendly approaches available. We developed a scalable version of the REMST protocol and showed numerically that it is suitable for systems with more than 100 qubits, matching the size of current state-of-the-art systems. The REMST protocol was applied to superconducting qubit experiments, where we saw an improvement in reconstruction accuracy by a factor of up to 30. In Part III, we move our focus to optimal measurement strategies. Adaptive measurement strategies promise a quadratic improvement in the statistical fluctuation of pure and close-to-pure state reconstruction by dynamically optimizing measurement settings during sampling. We investigated whether these adaptive measurement strategies were viable in realistic experimental settings. We demonstrated both analytically and in numerical simulations that going from ideal readout to noisy readout disproportionally deteriorates the quality of the adaptive measurement strategy, to a point where no asymptotic benefit exists for adaptive measurements. These results not only deepen our understanding of readout processes in superconducting qubits but also provide concrete implementations of more robust quantum measurement and tomography protocols, offering clearer insight into the interplay between readout noise and information extraction.