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Paper 1
Transversal Toffoli-gate in Hybrid-code System
Dawei Jiao, Mahdi Bayanifar, Alexei Ashikhmin, Olav Tirkkonen
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2511.09265
- arXiv
- 2511.09265
We study the transversality of the Toffoli gate in a hybrid-code system that employs two quantum error correction codes with special structure. We find that a system using a triorthogonal code with its paired code supports a fully transversal implementation of the Toffoli gate. Through circuit-level analysis, we prove the transversality of the Toffoli operation in this system. Based on this hybrid-code framework, we propose a Toffoli state distillation protocol that does not rely on pre-distilled $\mathbf{T}$-gate magic states. In our approach, the Toffoli state is directly distilled layer by layer within the hybrid-code system using only transversal operations. Numerical simulations demonstrate that our method uses approximately 50\% fewer qubit resources than previously reported protocols.
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Quantum circuit design for accurate simulation of qudit channels
Dong-Sheng Wang, Barry C. Sanders
- Year
- 2014
- Journal
- arXiv preprint
- DOI
- arXiv:1407.7251
- arXiv
- 1407.7251
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm distance. The classical algorithm is constructed by decomposing a quantum channel into a convex combination of generalized extreme channels by optimization of a set of nonlinear coupled algebraic equations. The resultant circuit is a randomly chosen generalized extreme channel circuit whose run-time is logarithmic with respect to the error tolerance and quadratic with respect to Hilbert space dimension, which requires only a single ancillary qudit plus classical dits.
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