Unifying and benchmarking state-of-the-art quantum error mitigation techniques

Abstract

Error mitigation is an essential component of achieving a practical quantum advantage in the near term, and a number of different approaches have been proposed. In this work, we recognize that many state-of-the-art error mitigation methods share a common feature: they are data-driven, employing classical data obtained from runs of different quantum circuits. For example, Zero-noise extrapolation (ZNE) uses variable noise data and Clifford-data regression (CDR) uses data from near-Clifford circuits. We show that Virtual Distillation (VD) can be viewed in a similar manner by considering classical data produced from different numbers of state preparations. Observing this fact allows us to unify these three methods under a general data-driven error mitigation framework that we call UNIfied Technique for Error mitigation with Data (UNITED). In certain situations, we find that our UNITED method can outperform the individual methods (i.e., the whole is better than the individual parts). Specifically, we employ a realistic noise model obtained from a trapped ion quantum computer to benchmark UNITED, as well as other state-of-the-art methods, in mitigating observables produced from random quantum circuits and the Quantum Alternating Operator Ansatz (QAOA) applied to Max-Cut problems with various numbers of qubits, circuit depths and total numbers of shots. We find that the performance of different techniques depends strongly on shot budgets, with more powerful methods requiring more shots for optimal performance. For our largest considered shot budget ($10^{10}$), we find that UNITED gives the most accurate mitigation. Hence, our work represents a benchmarking of current error mitigation methods and provides a guide for the regimes when certain methods are most useful.

25 pages, 11 figures, extended theoretical and numerical results, accepted by Quantum

References in corpus (17)

• Variational Quantum Algorithms
• Hybrid quantum-classical algorithms and quantum error mitigation
• Virtual Distillation for Quantum Error Mitigation
• Mitigating depolarizing noise on quantum computers with noise-estimation circuits
• Exponential Error Suppression for Near-Term Quantum Devices
• Simple Mitigation of Global Depolarizing Errors in Quantum Simulations
• Unified approach to data-driven quantum error mitigation
• Generalized quantum subspace expansion
• Extending quantum probabilistic error cancellation by noise scaling
• Quantum Error Mitigation using Symmetry Expansion
• The Dominant Eigenvector of a Noisy Quantum State
• Dual-state purification for practical quantum error mitigation
• Simulating quench dynamics on a digital quantum computer with data-driven error mitigation
• Quantum Error Mitigation Relying on Permutation Filtering
• Error mitigation by training with fermionic linear optics
• Resource-efficient Purification-based Quantum Error Mitigation
• Qubit-efficient exponential suppression of errors

Cited by in corpus (21)

• Quantum Error Mitigation
• Biology and medicine in the landscape of quantum advantages
• Extending quantum probabilistic error cancellation by noise scaling
• Universal Sampling Lower Bounds for Quantum Error Mitigation
• Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?
• Quantum Error Mitigation Relying on Permutation Filtering
• Volumetric Benchmarking of Error Mitigation with Qermit
• A Practical Framework for Quantum Error Mitigation
• Quantum error mitigation in the regime of high noise using deep neural network: Trotterized dynamics
• Enhancing qubit readout with Bayesian Learning
• Multireference error mitigation for quantum computation of chemistry
• Para-particle oscillator simulations on a trapped ion quantum computer
• Improving the efficiency of learning-based error mitigation
• Quantum Tunneling: From Theory to Error-Mitigated Quantum Simulation
• Echo-evolution data generation for quantum error mitigation via neural networks
• Spacetime quantum mechanics for bosonic and fermionic systems
• Superdiffusion resilience in Heisenberg Chains with 2D interactions on a quantum processor
• Quantum data generation in a denoising model with multiscale entanglement renormalization network
• Noisy Monitored Quantum Circuits
• Error-Mitigated Quantum Random Access Memory
• Error-Mitigated Multi-Layer Quantum Routing