[4] If you like operator dynamics, symmetries, or making classical simulations suffer a little less, have a look. Comments welcome :)
Code is open-source too (e.g. see our example notebook: lnkd.in/eP9_MKV4).
[3] Practically, this makes Pauli propagation more stable and more accurate under truncation and noise, and lets us push simulations further (e.g. Ising chains and all-to-all Heisenberg dynamics) with the same compute budget.
[2] The idea is to merge Pauli strings related by symmetry and only propagate one representative per orbit. Group theory does the bookkeeping; memory usage drops by a factor set by the symmetry size.
[1] Pauli propagation is a useful way to classically simulate quantum dynamics — until the number of Pauli strings explodes and your memory does the same.
In this paper, we ask a simple question: if the circuit has symmetry, why are we propagating the same Pauli strings over and over again?
Happy to share our paper: Leveraging Symmetry Merging in Pauli Propagation
scirate.com/arxiv/2512.1...
tl;dr We improve standard Pauli propagation by merging Pauli strings related by symmetry.
Shoutout to my collaborators @sueyeonchung.bsky.social @quantummanuel.bsky.social @qzoeholmes.bsky.social
❗New paper and open-source library❗
PauliPropagation.jl is your go-to library for simulating quantum circuits via Pauli propagation. Our paper provides a thorough overview of this new classical simulation method.
Paper: scirate.com/arxiv/2505.21606
Library: github.com/MSRudolph/PauliPropagation.jl
