monoprop: Scaling Pauli and Majorana propagation via Anticommutation Indices
Abstract
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 ∼1/N touch any given qubit or mode, and we use this to prove the time per gate scales as O(K/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 9.5×1010 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.
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BibTeX
@misc{miller2026monoprop,
title = {{monoprop: Scaling Pauli and Majorana propagation via Anticommutation Indices}},
author = {Aaron Miller},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21000},
eprint = {2610.21000},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21000},
}
RIS
TY - UNPB
TI - monoprop: Scaling Pauli and Majorana propagation via Anticommutation Indices
AU - Aaron Miller
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.21000
UR - https://arxiv.org/abs/2610.21000
AB - 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 ∼1/N touch any given qubit or mode, and we use this to prove the time per gate scales as O(K/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 9.5×10^10 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.
ER -