Comparative Study of Sampling-Based Simulation Costs of Noisy Quantum Circuits

Noise in quantum operations often negates the advantage of computation. However, most classical simulations computers calculate ideal probability amplitudes by either storing full state vectors or using sophisticated tensor-network contractions. Here we investigate sampling-based simulation methods for noisy circuits. Specifically, characterize costs two major schemes, stabilizer-state sampling magic states and Heisenberg propagation, circuits subject to stochastic Pauli noise, such as depolarizing dephasing noise. To this end, introduce several techniques reduce under It is revealed that low-noise regime, results a smaller cost, while propagation better high-noise regime. Furthermore, high noise rate approximately 10%, these provide scaling than given low-rank stabilizer decomposition. We believe knowledge useful achieve possible on near-term devices well efficient methods.