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

2026-05-18

AI Summary

Large multi-controlled Toffoli gates are challenging to implement efficiently in fault-tolerant quantum computing due to their high T-gate overhead. This work proposes a low T-depth decomposition method based on Clifford+T circuits, introducing for the first time a 4-input relative-phase Toffoli gate. By leveraging a single clean ancilla qubit, conditional measurement feedback, and dynamic uncomputation techniques, the approach significantly enhances parallelism while maintaining a low ancilla count and fixed T-count and CX-count. Experimental results demonstrate that the proposed method effectively reduces T-depth and outperforms existing schemes, making it well-suited for near-term noisy intermediate-scale quantum devices.

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.

Problem

• multi-controlled Toffoli
• T-depth
• Clifford+T decomposition
• ancilla qubit
• fault-tolerant quantum computing

Innovation

• adaptive decomposition
• relative-phase Toffoli
• T-depth reduction
• dynamic circuits
• ancilla-efficient