Leveraging Symmetry Merging in Pauli Propagation

TL;DR

This paper presents a symmetry-adapted method for simulating quantum dynamics that reduces computational complexity by merging Pauli strings related through symmetry, improving efficiency and stability in quantum simulations.

Contribution

The authors introduce a symmetry-merging Pauli propagation algorithm that exploits symmetries to reduce space complexity and enhance simulation stability.

Findings

Reduces space complexity by exploiting symmetry groups.

Improves numerical stability under truncation and noise.

Demonstrates practical benefits with open-source code.

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.