Qin, DayueChen, YanzhuLi, Ying2023-08-312023-08-312023-0435http://hdl.handle.net/10919/116175Quantum computing promises advantages over classical computing in many problems. Nevertheless, noise in quantum devices prevents most quantum algorithms from achieving the quantum advantage. Quantum error mitigation provides a variety of protocols to handle such noise using minimal qubit resources. While some of those protocols have been implemented in experiments for a few qubits, it remains unclear whether error mitigation will be effective in quantum circuits with tens to hundreds of qubits. In this paper, we apply statistics principles to quantum error mitigation and analyse the scaling behaviour of its intrinsic error. We find that the error increases linearly O(epsilon N) with the gate number N before mitigation and sublinearly O(epsilon'N-gamma) after mitigation, where gamma approximate to 0.5, epsilon is the error rate of a quantum gate, and epsilon' is a protocol-dependent factor. The root N scaling is a consequence of the law of large numbers, and it indicates that error mitigation can suppress the error by a larger factor in larger circuits. We propose the importance Clifford sampling as a key technique for error mitigation in large circuits to obtain this result.application/pdfenCreative Commons Attribution 4.0 InternationalArticle - Refereedhttps://doi.org/10.1038/s41534-023-00707-7912056-6387