Abstract
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.
Highlights
With the experimental demonstration of quantum supremacy [1], whether current or near-future noisy intermediate-scale quantum (NISQ) devices are sufficient for realizing quantum advantages in practical problems becomes one of the most exciting challenges in quantum computing [2]
We first introduce the background of analog quantum simulation (AQS) and digital quantum simulation (DQS) with noisy operations
While previous error-mitigation methods for DQS regard each gate as one entity and noise as an error channel before or after the gate, such a description becomes inadequate when the quantum gate is on multiqubits and the noise are inherently mixed in the realization of the quantum gate
Summary
With the experimental demonstration of quantum supremacy [1], whether current or near-future noisy intermediate-scale quantum (NISQ) devices are sufficient for realizing quantum advantages in practical problems becomes one of the most exciting challenges in quantum computing [2]. QEM method is one of the most effective techniques [4,5], which fully inverts noise effect by requiring a full tomography of the noise process and assuming noise independently appears either before or after each gate in a digital gatebased quantum computer While these assumptions are adopted for many QEM schemes, realistic noise is more complicated. As one of the major noises in superconducting qubits, crosstalk of multiqubit gates originates from the imperfect time evolution with unwanted interactions [31,32,33,38,39,40] Such inherent dynamics-based and nonlocal noise effects make conventional QEM schemes less effective for practical NISQ devices. We conduct a resource estimation for nearterm devices involving up to 100 qubits and show the feasibility of our QEM scheme in the NISQ regime
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