Error statistics and scalability of quantum error mitigation formulas

Abstract Quantum computing promises advantages over classical in many problems. Nevertheless, noise quantum devices prevents most algorithms from achieving the advantage. error mitigation provides a variety of protocols to handle such using minimal qubit resources. While some those have been implemented experiments for few qubits, it remains unclear whether will be effective circuits with tens hundreds qubits. In this paper, we apply statistics principles and analyse scaling behaviour its intrinsic error. We find that increases linearly O ( ϵ N ) gate number before sublinearly $$O({\epsilon }^{{\prime} }{N}^{\gamma })$$ O ( ϵ ′ N γ ) after mitigation, where γ ≈ 0.5, is rate gate, $${\epsilon }$$ protocol-dependent factor. The $$\sqrt{N}$$ consequence law large numbers, indicates can suppress by larger factor circuits. propose importance Clifford sampling as key technique obtain result.