Measurement-Driven Adaptive Low-Overhead Implementation of Multi-Controlled Toffoli Gates
This work addresses the resource overhead of non-Clifford operations in quantum computing, offering improved efficiency for quantum arithmetic and reversible logic in both near-term and fault-tolerant architectures.
The paper proposes dynamic decomposition strategies for multi-controlled Toffoli gates using mid-circuit measurement and classical feedforward, achieving reductions in entangling-gate count, T-count, and T-depth compared to static decompositions.
The Toffoli gate is a fundamental building block for quantum arithmetic and reversible logic, yet its efficient realization remains a major challenge in both near-term and fault-tolerant quantum architectures. Recent advances in dynamic quantum circuit capabilities, including mid-circuit measurement and classical feedforward, provide new opportunities for reducing the resource overhead of non-Clifford operations. In this work, we propose a set of dynamic decomposition strategies for multi-controlled Toffoli gates that exploit adaptive circuit execution and ancilla-assisted constructions. Our methods systematically reduce entangling-gate count, T-count, and T-depth compared with conventional static decompositions, while preserving fault-tolerance guarantees. Through analytical cost models and experimental evaluation, we demonstrate that relative-phase primitives and measurement-conditioned corrections enable scalable implementations with improved depth and resource efficiency.