SymPhase: Phase Symbolization for Fast Simulation of Stabilizer Circuits

This paper proposes an efficient stabilizer circuit simulation algorithm that only traverses the circuit forward once. We introduce phase symbolization into stabilizer generators, which allows possible Pauli faults in the circuit to be accumulated explicitly as symbolic expressions in the phases of stabilizer generators. This way, the measurement outcomes are also symbolic expressions, and we can sample them by substituting the symbolic variables with concrete values, without traversing the circuit repeatedly. We show how to integrate symbolic phases into the stabilizer tableau and maintain them efficiently using bit-vector encoding. A new data layout of the stabilizer tableau in memory is proposed, which improves the performance of our algorithm (and other stabilizer simulation algorithms based on the stabilizer tableau). We implement our algorithm and data layout in a Julia package named SymPhase.jl, and compare it with Stim, the state-of-the-art simulator, on several benchmarks. We show that SymPhase.jl has superior performance in terms of sampling time, which is crucial for generating a large number of samples for further analysis.