  Quantum 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 sub-linearly
$O(\epsilon' N^\gamma)$ after mitigation, where $\gamma \approx 0.5$,
$\epsilon$ is the error rate of a quantum gate, and $\epsilon'$ is a
protocol-dependent factor. The $\sqrt{N}$ 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.
