Quantum error mitigation is an important technique to reduce the impact of noise in quantum computers. With more and more qubits being supported on quantum computers, there are two emerging fundamental challenges. First, the number of shots required for quantum algorithms with large numbers of qubits needs to increase in order to obtain a meaningful distribution or expected value of an observable. Second, although steady progress has been made in improving the fidelity of each qubit, circuits with a large number of qubits are likely to produce erroneous results. This low-shot, high-noise regime calls for highly scalable error mitigation techniques. In this paper, we propose a simple and effective mitigation scheme, qubit-wise majority vote, for quantum algorithms with a single correct output. We show that our scheme produces the maximum likelihood (ML) estimate under certain assumptions, and bound the number of shots required. Our experimental results on real quantum devices confirm that our proposed approach requires fewer shots than existing ones, and can sometimes recover the correct answers even when they are not observed from the measurement results.

翻译：量子误差缓解是减少量子计算机中噪声影响的重要技术。随着量子计算机支持越来越多的量子比特，两个基本挑战逐渐显现。首先，为获得有意义的可观测量分布或期望值，大量子比特量子算法所需的采样次数需要增加。其次，尽管每个量子比特的保真度在稳步提升，但含大量子比特的线路仍可能产生错误结果。这种低采样、高噪声的现状亟需高度可扩展的误差缓解技术。本文针对具有单一正确输出的量子算法，提出一种简单有效的缓解方案——量子比特逐位多数投票法。我们证明，该方案在特定假设下能给出最大似然(ML)估计，并界定了所需采样次数。在真实量子设备上的实验结果表明，所提方法所需采样次数少于现有方案，且即使测量结果中未观测到正确答案时，有时也能恢复正确结果。