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arXiv:2302.05457 · Physical review. B./Physical review. B

Compressed quantum error mitigation

Maurits S. J. Tepaske, David J. Luitz

Published May 22, 2023• 4 citations
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Abstract

We introduce a quantum error mitigation technique based on probabilistic error cancellation to eliminate errors which have accumulated during the application of a quantum circuit. Our approach is based on applying an optimal ``denoiser'' after the action of a noisy circuit and can be performed with an arbitrary number of extra gates. The denoiser is given by an ensemble of circuits distributed with a quasiprobability distribution. For a simple noise model, we show that efficient, local denoisers can be found and we demonstrate their effectiveness for the digital quantum simulation of the time evolution of simple spin chains.

DOI
10.1103/physrevb.107.l201114

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We introduce a quantum error mitigation technique based on probabilistic error cancellation to eliminate errors which have accumulated during the application of a quantum circuit. Our approach is based on applying an optimal ``denoiser'' after the action of a noisy circuit and can be performed with an arbitrary number of extra gates. The denoiser is given by an ensemble of circuits distributed with a quasiprobability distribution. For a simple noise model, we show that efficient, local denoisers can be found and we demonstrate their effectiveness for the digital quantum simulation of the time evolution of simple spin chains.
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.
Using near-term quantum computers to achieve a quantum advantage requires efficient strategies to improve the performance of the noisy quantum devices presently available. We develop and experimentally validate two efficient error mitigation protocols named ``Noiseless Output Extrapolation" and ``Pauli Error Cancellation" that can drastically enhance the performance of quantum circuits composed of noisy cycles of gates. By combining popular mitigation strategies such as probabilistic error cancellation and noise amplification with efficient noise reconstruction methods, our protocols can mitigate a wide range of noise processes that do not satisfy the assumptions underlying existing mitigation protocols, including non-local and gate-dependent processes. We test our protocols on a four-qubit superconducting processor at the Advanced Quantum Testbed. We observe significant improvements in the performance of both structured and random circuits, with up to 86% improvement in variation distance over the unmitigated outputs. Our experiments demonstrate the effectiveness of our protocols, as well as their practicality for current hardware platforms.
In the era of noisy intermediate-scale quantum devices, the number of controllable hardware qubits is insufficient to implement quantum error correction.As an alternative, quantum error mitigation (QEM) can suppress errors in measurement results via repeated experiments and postprocessing of data.Typical techniques for error mitigation, e.g., the quasiprobability decomposition method, ignore correlated errors between different gates.Here, we introduce a QEM method based on the matrix product operator (MPO) representation of a quantum circuit that can characterize the noise channel with polynomial complexity.Our technique is demonstrated on a depth = 20 fully parallel quantum circuit of up to N q = 20 qubits undergoing local and global noise.The circuit error is reduced by a several-times factor with only a small bond dimension D = 1 for the noise channel.The MPO representation increases the accuracy of modeling noise without consuming more experimental resources, which improves the QEM performance and broadens its scope of application.Our method is hopeful of being applied to circuits in higher dimensions with more qubits and deeper depth.
Quantum systems are inherently open and susceptible to environmental noise, which can have both detrimental and beneficial effects on their dynamics.This phenomenon has been observed in biomolecular systems, where noise enables novel functionalities, making the simulation of their dynamics a crucial target for digital and analog quantum simulation.Nevertheless, the computational capabilities of current quantum devices are often limited due to their inherent noise.In this work, we present a novel approach that capitalizes on the intrinsic noise of quantum devices to reduce the computational resources required for simulating open quantum systems.Our approach combines quantum noise characterization methods with quantum error mitigation techniques, enabling us to manipulate and control the intrinsic noise in a quantum circuit.Specifically, we selectively enhance or reduce decoherence rates in the quantum circuit to achieve the desired simulation of open-system dynamics.We provide a detailed description of our methods and report on the results of noise characterization and quantum error mitigation experiments conducted on both real and emulated IBM Quantum computers.Additionally, we estimate the experimental resource requirements for our techniques.Our approach holds the potential to unlock new simulation techniques in noisy intermediate-scale quantum devices, harnessing their intrinsic noise to enhance quantum computations.
Quantum error mitigation (QEM) is vital for noisy intermediate-scale quantum (NISQ) devices. While most conventional QEM schemes assume discrete gate-based circuits with noise appearing either before or after each gate, the assumptions are inappropriate for describing realistic noise that may have strong gate dependence and complicated nonlocal effects, and general computing models such as analog quantum simulators. To address these challenges, we first extend the scenario, where each computation process, being either digital or analog, is described by a continuous time evolution. For noise from imperfections of the engineered Hamiltonian or additional noise operators, we show it can be effectively suppressed by a stochastic QEM method. Since our method assumes only accurate single qubit controls, it is applicable to all digital quantum computers and various analog simulators. Meanwhile, errors in the mitigation procedure can be suppressed by leveraging the Richardson extrapolation method. As we numerically test our method with various Hamiltonians under energy relaxation and dephasing noise and digital quantum circuits with additional two-qubit crosstalk, we show an improvement of simulation accuracy by 2 orders. We assess the resource cost of our scheme and conclude the feasibility of accurate quantum computing with NISQ devices.
Abstract Various quantum applications can be reduced to estimating expectation values, which are inevitably deviated by operational and environmental errors. Although errors can be tackled by quantum error correction, the overheads are far from being affordable for near-term technologies. To alleviate the detrimental effects of errors on the estimation of expectation values, quantum error mitigation techniques have been proposed, which require no additional qubit resources. Here we benchmark the performance of a quantum error mitigation technique based on probabilistic error cancellation in a trapped-ion system. Our results clearly show that effective gate fidelities exceed physical fidelities, i.e., we surpass the break-even point of eliminating gate errors, by programming quantum circuits. The error rates are effectively reduced from (1.10 ± 0.12) × 10−3 to (1.44 ± 5.28) × 10−5 and from (0.99 ± 0.06) × 10−2 to (0.96 ± 0.10) × 10−3 for single- and two-qubit gates, respectively. Our demonstration opens up the possibility of implementing high-fidelity computations on a near-term noisy quantum device.