# Simulation of Qubit Quantum Circuits via Pauli Propagation

## TL;DR

This paper introduces efficient algorithms for simulating qubit quantum circuits, including Clifford circuits in linear time, and identifies classes of non-stabilizer states that can be simulated efficiently, outperforming previous methods.

## Contribution

The authors develop novel algorithms that enable linear-time simulation of Clifford circuits and expand the class of simulatable states beyond stabilizer states.

## Key findings

- Clifford circuits can be simulated in linear time.
- New algorithms outperform previous noisy near-Clifford techniques.
- Efficient simulation of a large class of non-stabilizer states.

## Abstract

We present novel algorithms to estimate outcomes for qubit quantum circuits. Notably, these methods can simulate a Clifford circuit in linear time without ever writing down stabilizer states explicitly. These algorithms outperform previous noisy near-Clifford techniques for most circuits. We identify a large class of input states that can be efficiently simulated despite not being stabilizer states. The algorithms leverage probability distributions constructed from Bloch vectors, paralleling previously known algorithms that use the discrete Wigner function for qutrits.