Fault-Tolerant Quantum Computation (FTQC) permits parallel execution of mutually commuting Pauli Product Rotations (PPRs), but per-qubit access point/port limits (e.g. two X and two Z edges on the surface code) force commuting groups that exceed the budget to be split, inflating circuit depth. We propose two heuristics for reducing this hardware-limited depth: 1. clique reshuffling, which permutes commuting products and re-forms port-constrained groups, and 2. generator restructuring, which rewrites each group as an equivalent generating set with reduced per-qubit port pressure. On QASMBench circuits compiled to PPRs, we combine the two heuristics and observe an average hardware-limited depth reduction of 10−20% over a non-reordering baseline, with up to 50% reduction. These observed gains scale with the per-qubit port budget and saturate near 20 ports, suggesting these heuristics remain relevant as hardware exposes more access points.
@article{arxiv.2605.23738,
title = {Optimizing Parallel Execution of Commuting Pauli Product Rotations},
author = {Sayam Sethi and Devika Nambisan and Jonathan Mark Baker},
journal= {arXiv preprint arXiv:2605.23738},
year = {2026}
}