[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?