Abstract

Measurement noise is one of the main sources of errors in currently available quantum devices based on superconducting qubits. At the same time, the complexity of its characterization and mitigation often exhibits exponential scaling with the system size. In this work, we introduce a correlated measurement noise model that can be efficiently described and characterized, and which admits effective noise-mitigation on the level of marginal probability distributions. Noise mitigation can be performed up to some error for which we derive upper bounds. Characterization of the model is done efficiently using Diagonal Detector Overlapping Tomography – a generalization of the recently introduced Quantum Overlapping Tomography to the problem of reconstruction of readout noise with restricted locality. The procedure allows to characterizek-local measurement cross-talk onN-qubit device usingO(k2klog(N))circuits containing random combinations of X and identity gates. We perform experiments on 15 (23) qubits using IBM's (Rigetti's) devices to test both the noise model and the error-mitigation scheme, and obtain an average reduction of errors by a factor>22(>5.5) compared to no mitigation. Interestingly, we find that correlations in the measurement noise do not correspond to the physical layout of the device. Furthermore, we study numerically the effects of readout noise on the performance of the Quantum Approximate Optimization Algorithm (QAOA). We observe in simulations that for numerous objective Hamiltonians, including random MAX-2-SAT instances and the Sherrington-Kirkpatrick model, the noise-mitigation improves the quality of the optimization. Finally, we provide arguments why in the course of QAOA optimization the estimates of the local energy (or cost) terms often behave like uncorrelated variables, which greatly reduces sampling complexity of the energy estimation compared to the pessimistic error analysis. We also show that similar effects are expected for Haar-random quantum states and states generated by shallow-depth random circuits.

Highlights

  • 1.1 MotivationOutstanding progress has been made in the last years on the path to development of scalable and Accepted in Quantum 2021-05-18, click title to verify

  • We introduce notion of Diagonal Detector Overlapping Tomography (DDOT) which allows to reconstruct noise description with k-local cross-talk on N -qubit device using O k2k log (N ) quantum circuits consisting of single layer of X and identity gates

  • The basic idea of the model is to group qubits into strongly-correlated clusters that are mildly affected by their neighborhoods, which, provided that the size of those groups is bounded by a constant, allows to describe a global noise model by much smaller number of parameters compared to the most generic situation

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Summary

Introduction

1.1 MotivationOutstanding progress has been made in the last years on the path to development of scalable and Accepted in Quantum 2021-05-18, click title to verify. As quantum devices in the near-term will be unable to implement proper error correction [5], various methods of noise mitigation have been recently developed [6,7,8,9,10,11,12,13,14,15]. Those methods aim at reducing the effects of errors present in quantum gates and/or in quantum measurements. We focus on the latter, i.e., noise affecting quantum detectors

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