Leveraging Symmetry Merging in Pauli Propagation

• URL: http://arxiv.org/abs/2512.12094v1
• Date: Fri, 12 Dec 2025 23:51:02 GMT
• Title: Leveraging Symmetry Merging in Pauli Propagation
• Authors: Yanting Teng, Su Yeon Chang, Manuel S. Rudolph, Zoë Holmes,
• Abstract summary: We introduce a symmetry-adapted framework for simulating quantum dynamics based on Pauli propagation.<n>We exploit this by merging Pauli strings related through symmetry transformations.<n>We show that symmetry merging reduces space complexity by a factor set by orbit sizes, with explicit gains for translation and permutation symmetries.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a symmetry-adapted framework for simulating quantum dynamics based on Pauli propagation. When a quantum circuit possesses a symmetry, many Pauli strings evolve redundantly under actions of the symmetry group. We exploit this by merging Pauli strings related through symmetry transformations. This procedure, formalized as the symmetry-merging Pauli propagation algorithm, propagates only a minimal set of orbit representatives. Analytically, we show that symmetry merging reduces space complexity by a factor set by orbit sizes, with explicit gains for translation and permutation symmetries. Numerical benchmarks of all-to-all Heisenberg dynamics confirm improved stability, particularly under truncation and noise. Our results establish a group-theoretic framework for enhancing Pauli propagation, supported by open-source code demonstrating its practical relevance for classical quantum-dynamics simulations.

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