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arXiv:2001.09980 · Quantum Science and Technology

Toward efficient correction of multiqubit measurement errors: pair correlation method

Michael R Geller, Mingyu Sun

Published Dec 22, 2020• 63 citations
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Abstract

Abstract Measurement errors limit the performance of near-term quantum computers and their potential for practical application. However they are partly correctable after a calibration step that requires, for a complete implementation on a register of n qubits, 2 n additional measurements. Here we introduce an approximate but efficient method for multiqubit measurement error characterization and mitigation requiring the classical processing of 2 n × 2 n matrices, but only O (4 k n 2 ) measurements, where k = O (1) is the number of qubits in a correlation volume. We demonstrate and validate the method on an IBM Q processor with registers of 4 and 8 superconducting qubits.

DOI
10.1088/2058-9565/abd5c9

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Abstract Measurement errors limit the performance of near-term quantum computers and their potential for practical application. However they are partly correctable after a calibration step that requires, for a complete implementation on a register of n qubits, 2 n additional measurements. Here we introduce an approximate but efficient method for multiqubit measurement error characterization and mitigation requiring the classical processing of 2 n × 2 n matrices, but only O (4 k n 2 ) measurements, where k = O (1) is the number of qubits in a correlation volume. We demonstrate and validate the method on an IBM Q processor with registers of 4 and 8 superconducting qubits.
State preparation and measurement (SPAM) errors limit the performance of many gate-based quantum computing architecures, but are partly correctable after a calibration step that requires, for an exact implementation on a register of nnn qubits, 2n2^n2n additional characterization experiments, as well as classical post-processing. Here we introduce an approximate but efficient method for SPAM error characterization requiring the {\it classical} processing of 2n ⁣×2n2^n \! \times 2^n2n×2n real matrices, but only O(n2)O(n^2)O(n2) measurements. The technique assumes that multi-qubit measurement errors are dominated by pair correlations, which are estimated with n(n−1)k/2n(n-1)k/2n(n−1)k/2 two-qubit experiments, where kkk is a parameter related to the accuracy. We demonstrate the technique on the IBM and Rigetti online superconducting quantum computers, allowing comparison of their SPAM errors in both magnitude and degree of correlation. We also study the correlations as a function of the register's geometric layout. We find that the pair-correlation model is fairly accurate on linear arrays of superconducting qubits. However qubits arranged in more closely spaced two-dimensional geometries exhibit significant higher-order (such as 3-qubit) SPAM error correlations.
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.
Reducing measurement errors in multiqubit quantum devices is critical for performing any quantum algorithm. Here we show how to mitigate measurement errors by a classical postprocessing of the measured outcomes. Our techniques apply to any experiment where measurement outcomes are used for computing expected values of observables. Two error-mitigation schemes are presented based on tensor product and correlated Markovian noise models. Error rates parametrizing these noise models can be extracted from the measurement calibration data using a simple formula. Error mitigation is achieved by applying the inverse noise matrix to a probability vector that represents the outcomes of a noisy measurement. The error-mitigation overhead, including the number of measurements and the cost of the classical postprocessing, is exponential in $\ensuremath{\epsilon}n$, where $\ensuremath{\epsilon}$ is the maximum error rate and nnn is the number of qubits. We report experimental demonstration of our error-mitigation methods on IBM Quantum devices using stabilizer measurements for graph states with $n\ensuremath{\le}12$ qubits and entangled 20-qubit states generated by low-depth random Clifford circuits.
We develop a classical bit-flip correction method to mitigate measurement errors on quantum computers. This method can be applied to any operator, any number of qubits, and any realistic bit-flip probability. We first demonstrate the successful performance of this method by correcting the noisy measurements of the ground-state energy of the longitudinal Ising model. We then generalize our results to arbitrary operators and test our method both numerically and experimentally on IBM quantum hardware. As a result, our correction method reduces the measurement error on the quantum hardware by up to one order of magnitude. We finally discuss how to preprocess the method and extend it to other error sources beyond measurement errors. For local Hamiltonians, the overhead costs are polynomial in the number of qubits, even if multiqubit correlations are included.
A detailed understanding of the noise processes and errors in near-term quantum computers is essential for accurate calibration of gates, and for achieving optimal performance when executing near-term applications such as quantum chemistry, optimization, or machine learning problems. This paper introduces several sources of noise in superconducting qubit based quantum computers such as those deployed by IBM, describes some of the main techniques for characterizing the resulting errors, and for mitigating the effects of certain errors without access to quantum error correction. We demonstrate experimental application of these techniques on an IBM Quantum system using the open source Qiskit software library.
We introduce a technique for the suppression of state-dependent and correlated measurement errors, which are commonly observed on modern superconducting quantum devices. Our method leverages previous results, establishing that correlated errors tend to be physically localised on quantum devices to perform characterisations over the coupling map of the device, and to join overlapping measurement calibrations as a series of sparse matrices. We term this 'Coupling Map Calibration'. We quantitatively demonstrate the advantages of our proposed error mitigation system design across a range of current IBM quantum devices. Our experimental results on common benchmark circuits demonstrate up to a 41% reduction in the error rate without increasing the number of executions of the quantum device required when compared to conventional error mitigation methods.