# Unbiased Simulation of Near-Clifford Quantum Circuits

## TL;DR

This paper introduces a practical and accurate method for simulating noisy near-Clifford quantum circuits using quasiprobability distributions, enabling the study of larger and more realistic quantum systems.

## Contribution

The authors develop an unbiased simulation technique for noisy Clifford circuits based on quasiprobability representations, improving efficiency and accuracy over previous methods.

## Key findings

- Simulated a Steane [[7,1,3]]-encoded logical operation with non-Clifford errors.
- Computed the fault tolerance error threshold for the encoded operation.
- Demonstrated the method's potential for studying larger quantum circuits.

## Abstract

Modeling and simulation is essential for predicting and verifying the behavior of fabricated quantum circuits, but existing simulation methods are either impractically costly or require an unrealistic simplification of error processes. We present a method of simulating noisy Clifford circuits that is both accurate and practical in experimentally relevant regimes. In particular, the cost is weakly exponential in the size and the degree of non-Cliffordness of the circuit. Our approach is based on the construction of exact representations of quantum channels as quasiprobability distributions over stabilizer operations, which are then sampled, simulated, and weighted to yield unbiased statistical estimates of circuit outputs and other observables. As a demonstration of these techniques we simulate a Steane [[7,1,3]]-encoded logical operation with non-Clifford errors and compute its fault tolerance error threshold. We expect that the method presented here will enable studies of much larger and more realistic quantum circuits than was previously possible.