monoprop: Scaling Pauli and Majorana propagation via Anticommutation Indices

We introduce monoprop, an open-source, massively parallel operator-propagation framework for fermion and qubit bases. For $N$ qubits or modes, existing codes represent each of the $K$ tracked operator terms (Pauli strings or products of Majorana operators) as a $2N$-bit string, testing each for anticommutation with the gate at $O(KN)$ cost per gate. Here, we introduce the anticommutation index which rapidly looks up the terms anticommuting with a gate. A local gate changes only the terms that touch its sites, and when terms are truncated to act on few sites, only a fraction $\sim 1\mathrm{/}N$ touch any given qubit or mode, and we use this to prove the time per gate scales as $O(K\mathrm{/}N)$. This counterintuitive result tells us that for a fixed number of terms, increasing the number of sites can make things faster. We demonstrate this numerically, and show monoprop scales almost ideally to 8192 cores, tracking $9.5\times {10}^{10}$ terms. Beyond propagation, we present memory-efficient surrogate graphs, which record one propagation and replay it at new angles, for fast energy re-estimation and parameter gradients, and an efficient method for finding energy-minimising gates and optimal angles for simulating adaptive quantum-chemistry circuits.