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

Abstract

There have been intensive efforts to develop quantum computers, and the number of qubits is now reaching around 50 qubits. In practice, not only the number of qubits but the fidelity of the gates and measurements plays an important role. The noise in quantum operations often damages the advantage of quantum computation. However, most classical simulations of quantum computers calculate the ideal probability amplitudes either storing full state vectors or using sophisticated tensor network contractions, where noise is not employed to relax classical simulation costs. In this work, we investigate simulation costs of noisy quantum circuits based on two major sampling-based simulation algorithms, stabilizer-state sampling and Heisenberg propagation. To this end, we improve the existing stabilizer-state sampling algorithm based on robustness of magic so that the simulation costs are reduced even under noise on Clifford gates. We compared the simulation costs and clarified when one algorithm outperforms the other. In addition, we calculated the simulation costs of a noisy single-qubit rotation gate and confirmed that small noise makes the noisy rotation gate efficiently simulatable, as expected. These results are useful to design quantum circuits, which potentially have quantum advantages.