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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.

Paper 2

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