Adaptive Clifford+T Decomposition of Large Toffoli Gates with One Clean Ancilla
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911693974536192 |
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| author | Kole, Abhoy Assaad, Majd Schnittka, Till Drechsler, Rolf |
| author_facet | Kole, Abhoy Assaad, Majd Schnittka, Till Drechsler, Rolf |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18169 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive Clifford+T Decomposition of Large Toffoli Gates with One Clean Ancilla Kole, Abhoy Assaad, Majd Schnittka, Till Drechsler, Rolf Quantum Physics Emerging Technologies 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. |
| title | Adaptive Clifford+T Decomposition of Large Toffoli Gates with One Clean Ancilla |
| topic | Quantum Physics Emerging Technologies |
| url | https://arxiv.org/abs/2605.18169 |