Stim: a fast stabilizer circuit simulator

TL;DR

Stim is a highly efficient stabilizer circuit simulator capable of analyzing large quantum circuits rapidly by leveraging advanced data structures and SIMD instructions, enabling quick sampling and analysis of complex quantum systems.

Contribution

Stim introduces three key improvements to stabilizer simulation: linear measurement complexity, cache-friendly data layout, and bulk sampling using reference states, significantly enhancing speed and scalability.

Findings

Analyzes a 20,000-qubit surface code in 15 seconds

Samples at a rate of 1,000 shots per second

Outperforms existing stabilizer simulators in speed and efficiency

Abstract

This paper presents ``Stim", a fast simulator for quantum stabilizer circuits. The paper explains how Stim works and compares it to existing tools. With no foreknowledge, Stim can analyze a distance 100 surface code circuit (20 thousand qubits, 8 million gates, 1 million measurements) in 15 seconds and then begin sampling full circuit shots at a rate of 1 kHz. Stim uses a stabilizer tableau representation, similar to Aaronson and Gottesman's CHP simulator, but with three main improvements. First, Stim improves the asymptotic complexity of deterministic measurement from quadratic to linear by tracking the {\em inverse} of the circuit's stabilizer tableau. Second, Stim improves the constant factors of the algorithm by using a cache-friendly data layout and 256 bit wide SIMD instructions. Third, Stim only uses expensive stabilizer tableau simulation to create an initial reference sample. Further samples are collected in bulk by using that sample as a reference for batches of Pauli frames propagating through the circuit.