Simulating Quantum Circuits by Shuffling Paulis

TL;DR

This paper introduces an efficient classical simulation algorithm for noisy stabilizer quantum circuits, capable of handling complex mixed states and outperforming previous methods especially in depolarizing noise scenarios.

Contribution

The authors develop a novel stabilizer-based simulation algorithm that can simulate a broader class of quantum states, including bound states, and is faster for circuits with depolarizing noise.

Findings

Efficient simulation of noisy stabilizer circuits achieved.

Simulation of multi-qubit mixed states beyond stabilizer mixtures.

Faster simulation performance for circuits with depolarizing noise.

Abstract

Verification of NISQ era quantum devices demands fast classical simulation of large noisy quantum circuits. We present an algorithm based on the stabilizer formalism that can efficiently simulate noisy stabilizer circuits. Additionally, the protocol can efficiently simulate a large set of multi-qubit mixed states that are not mixtures of stabilizer states. The existence of these 'bound states' was previously only known for odd-dimensional systems like qutrits. The algorithm also has the favorable property that circuits with depolarizing noise are simulated much faster than unitary circuits. This work builds upon a similar algorithm by Bennink et al. (Phys. Rev. A 95, 062337) and utilizes a framework by Pashayan et al. (Phys. Rev. Lett. 115, 070501).