The paper combines two complementary techniques. First, Hadamard degadgetization removes auxiliary gadget wires, yielding ancilla-free circuits that reflect the true logical qubit count. Second, a ZX pathwidth–guided reduction merges overlapping spiders to eliminate qubits while preserving functional correctness and T-count. These steps are applied to circuits that have already passed through the FastTMerge → InternalHOpt → gadgetization → FastTODD chain, ensuring that T-depth and T-count remain optimized while qubit count is minimized.
All circuits originate from the benchmarking suite used in Vandaele’s study, incorporating reversible logic benchmarks sourced from
Dmitri Maslov. Reversible Logic Synthesis Benchmarks page — http://webhome.cs.uvic.ca/~dmaslov. Each circuit in the Parquet file is the serialized
.qc output produced after the pre-optimization pipeline (FastTMerge → InternalHOpt → gadgetization → FastTODD) but before Hadamard degadgetization and ZX pathwidth reduction, providing a faithful snapshot of the inputs to the ZX-calculus qubit-count optimization procedure.