Error Mitigation for Short-Depth Quantum Circuits.

By Kristan Temme, Sergey Bravyi, Jay M. Gambetta. Physical Review Letters, 2016

1,433 citations recorded by the source corpus.

Two schemes are presented that mitigate the effect of errors and decoherence in short-depth quantum circuits. The size of the circuits for which these techniques can be applied is limited by the rate at which the errors in the computation are introduced. Near-term applications of early quantum devices, such as quantum simulations, rely on accurate estimates of expectation values to become relevant. Decoherence and gate errors lead to wrong estimates of the expectation values of observables used to evaluate the noisy circuit. The two schemes we discuss are deliberately simple and do not require additional qubit resources, so to be as practically relevant in current experiments as possible. The first method, extrapolation to the zero noise limit, subsequently cancels powers of the noise perturbations by an application of Richardson's deferred approach to the limit. The second method cancels errors by resampling randomized circuits according to a quasiprobability distribution.

Subfields: Artificial Intelligence, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/04976cb176d0c128e244c04215be13d27df2b5b1

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Citations in the corpus

Supervised learning with quantum-enhanced feature spaces (2018, methodology): “In all experiments throughout this work we implemented an error mitigation technique which relies on zero-noise extrapolation to ﬁrst order [10, 25].”
The future of quantum computing with superconducting qubits (2022, methodology): “Probabilistic error cancellation (PEC) 10,72 aims to approximate an ideal quantum circuit via a weighted sum of noisy circuits that can be implemented on a given quantum computer.”
Quantum Simulators: Architectures and Opportunities (2019, background): “Because quantum simulators do not demand the same flexibility as universal quantum computers, they open up the possibility to devise error mitigation schemes that are targeted at special purpose simulations with near-term devices [114–117].”
Variational quantum algorithms (2020, methodology): “First, Richardson extrapolation was proposed [74, 89, 205], and it was shown that single- and multi-exponential extrapolation work well for Markovian gate errors, with the latter subsequently shown to have very broad efficacy [206, 207].”
QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits (2021, methodology): “Extrapolation methods [115], [116] perform multiple measurements under different error rates and extrapolate ideal measurement outcomes when no noise.”
Practical Quantum Error Mitigation for Near-Future Applications (2017, methodology): “[14] is that one can exactly compensate for the effect of errors by sampling from a set of (real, error-burdened) circuits, each labeled OðlÞ tot for l 1⁄4 1; 2;.”
Digital zero noise extrapolation for quantum error mitigation (2020, methodology): “There are many examples of error-mitigating techniques, including probabilistic error cancellation [5], [6], randomized compiling [7], Pauli-frame randomization [8], dynamical decoupling [9]–[12], quantum optimal control [13], [14], etc.”
Fundamental limits of quantum error mitigation (2021, methodology): “…circuit depth for the general error-mitigation protocol, conﬁrming a suspicion that the well-known exponential growing estimation error observed in several existing error-mitigation techniques [3, 26] is a consequence of the fundamental obstacle shared by the general error-mitigation strategies.”
Evidence for the utility of quantum computing before fault tolerance (2023, background): “based on pulse stretching 9,17,18 or subcircuit repetition 20–22 have circum-vented the need for precise noise learning, while relying on simplistic assumptions about the device noise.”
Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors (2022, methodology): “Although Λ − 1 is not a physical operation, it can be expressed as a linear combination of gates and state-preparation operations [9, 12].”
Barren plateaus in variational quantum computing (2024, neutral): “Thus, if one purifies 76,107 the noisy state ρ can become tractable for unitary parametrized quantum circuits (PQCs) under certain assumptions.”