Nontrivial Multiproduct 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 multiproduct commutation relation (MCR). MCR constructs gate sequences based on specific commutation properties among multi-Pauli operators, yielding seemingly noncommutative 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.