Adaptive Clifford+T Decomposition of Large Toffoli Gates with One Clean Ancilla

TL;DR

This paper presents an optimized method for decomposing large Toffoli gates using Clifford+T circuits with one clean ancilla, emphasizing T-depth reduction and resource efficiency.

Contribution

It introduces a novel decomposition approach utilizing 3- and 4-input relative-phase Toffoli gates with dynamic circuit techniques, achieving lower T-depth.

Findings

Significant T-depth reduction with 4-input relative-phase Toffoli gates.

Explicit resource bounds for Clifford+T implementations with a single clean ancilla.

Experimental validation shows improved efficiency over existing methods.

Abstract

Multi-controlled Toffoli gates are fundamental building blocks in quantum computation, with applications in quantum arithmetic, simulation, and search algorithms. In fault-tolerant architectures, their realization is constrained by the high cost of non-Clifford resources, particularly in terms of T-count and T-depth. Recent advances have demonstrated that the use of ancillary qubits, relative-phase Toffoli gates, and dynamic circuit techniques can substantially reduce this overhead. In this work, we investigate the decomposition of large Toffoli gates using 3- and 4-input relative-phase Toffoli gates in the presence of a single clean ancilla and conditionally clean ancillas. We derive explicit resource bounds for Clifford+T implementations incorporating dynamic-circuit-based uncomputation and measurement-conditioned corrections. Our analysis emphasizes T-depth reduction under fixed CX and T-count overhead, ensuring relevance for near-term devices. We show that introducing 4-input relative-phase Toffoli gates enables significant T-depth reductions through enhanced parallelism while maintaining favorable ancilla requirements. We further validate our theoretical results through experimental evaluation and comparative analysis with existing approaches.