Stim: a fast stabilizer circuit simulator

Craig Gidney

Google Inc., Santa Barbara, California 93117, USA

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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 $inverse$ 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.

Quantum stabilizer circuits are simple enough to be efficiently simulated, but rich enough to represent important quantum effects like teleportation and error correction. Stim can analyze many stabilizer circuits tens of times faster than previous tools, and then collect samples tens of thousands of times faster than previous tools. This is useful because analyzing and simulating stabilizer circuits is a foundational part of quantum error correction research.

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► References

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