Nontrivial multi-product commutation relation toward reducing T-count in sequential Pauli-based computation

Abstract

Quantum compilers that reduce the number of T gates are essential for minimizing the overhead of fault-tolerant quantum computation. Achieving further T-count reduction calls for identifying equivalent circuit transformation rules beyond those utilized in existing tools. In this paper, we rewrite any given Clifford+T circuit using a Clifford block followed by a sequential Pauli-based computation, and introduce a nontrivial, ancilla-free transformation rule, the multi-product commutation relation (MCR). MCR constructs gate sequences based on specific commutation properties among multi-Pauli operators, yielding seemingly non-commutative instances that can be commuted, thereby enabling gate orderings that cannot be derived from pairwise commutation alone. To evaluate whether existing compilers account for this commutation rule, we create a benchmark circuit dataset using quantum circuit unoptimization. This approach intentionally adds redundancy to the circuit while keeping its equivalence, allowing a quantitative evaluation of compiler performance by comparison with the original circuit. Our numerical experiments reveal that the transformation rule based on MCR is not yet incorporated into current compilers, despite their demonstrated effectiveness for T-count reduction. These findings suggest an untapped potential for further T-count reduction by integrating MCR-aware transformations, paving the way for improvements in quantum compilers.