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

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. We also propose the MCR Compiler, which incorporates MCR-based transformations as an optimization pass. To evaluate its effect, we use a benchmark circuit dataset generated through 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 MCR Compiler achieves further T-count reduction beyond current compilers, establishing MCR-based transformations as a practical optimization primitive. These results highlight an untapped opportunity to enhance the optimization capabilities of quantum compilers.