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arXiv:2104.04607

Categorizing Readout Error Correlations on Near Term Quantum Computers

Benjamin Philip Nachman, Michael R. Geller

Published Apr 9, 2021• 5 citations
arXivHTMLPDF

Abstract

Readout errors are a significant source of noise for near term quantum computers. A variety of methods have been proposed to mitigate these errors using classical post processing. For a system with $n$ qubits, the entire readout error profile is specified by a $2^n\times 2^n$ matrix. Recent proposals to use sub-exponential approximations rely on small and/or short-ranged error correlations. In this paper, we introduce and demonstrate a methodology to categorize and quantify multiqubit readout error correlations. Two distinct types of error correlations are considered: sensitivity of the measurement of a given qubit to the state of nearby "spectator" qubits, and measurement operator covariances. We deploy this methodology on IBMQ quantum computers, finding that error correlations are indeed small compared to the single-qubit readout errors on IBMQ Melbourne (15 qubits) and IBMQ Manhattan (65 qubits), but that correlations on IBMQ Melbourne are long-ranged and do not decay with inter-qubit distance.

DOI
10.48550/arxiv.2104.04607

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Readout errors are a significant source of noise for near term quantum computers. A variety of methods have been proposed to mitigate these errors using classical post processing. For a system with nnn qubits, the entire readout error profile is specified by a 2n×2n2^n\times 2^n2n×2n matrix. Recent proposals to use sub-exponential approximations rely on small and/or short-ranged error correlations. In this paper, we introduce and demonstrate a methodology to categorize and quantify multiqubit readout error correlations. Two distinct types of error correlations are considered: sensitivity of the measurement of a given qubit to the state of nearby "spectator" qubits, and measurement operator covariances. We deploy this methodology on IBMQ quantum computers, finding that error correlations are indeed small compared to the single-qubit readout errors on IBMQ Melbourne (15 qubits) and IBMQ Manhattan (65 qubits), but that correlations on IBMQ Melbourne are long-ranged and do not decay with inter-qubit distance.
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.
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.
Current noisy quantum computers have multiple types of errors, which can occur in the state preparation, measurement/readout, and gate operation, as well as intrinsic decoherence and relaxation. Partly motivated by the booming of intermediate-scale quantum processors, measurement and gate errors have been recently extensively studied, and several methods of mitigating them have been proposed and formulated in software packages (e.g., in IBM Qiskit). Despite this, the state preparation error and the procedure to quantify it have not yet been standardized, as state preparation and measurement errors are usually considered not directly separable. Inspired by a recent work of Laflamme, Lin, and Mor \cite{laflamme2022algorithmic}, we propose a simple and resource-efficient approach to quantify separately the state preparation and readout error rates. With these two errors separately quantified, we also propose methods to mitigate them separately, especially mitigating state preparation errors with linear (with the number of qubits) complexity. As a result of the separate mitigation, we show that the fidelity of the outcome can be improved by an order of magnitude compared to the standard measurement error mitigation scheme. We also show that the quantification and mitigation scheme is resilient against gate noise and can be immediately applied to current noisy quantum computers. To demonstrate this, we present results from cloud experiments on IBM's superconducting quantum computers. The results indicate that the state preparation error rate is also an important metric for qubit metrology that can be efficiently obtained.
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.
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.