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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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Subwavelength vacuum lattices and atom-atom interactions in photonic crystals
A. González-Tudela, C. -L. Hung, D. E. Chang, J. I. Cirac, H. J. Kimble
- Year
- 2014
- Journal
- arXiv preprint
- DOI
- arXiv:1407.7336
- arXiv
- 1407.7336
We propose the use of photonic crystal structures to design subwavelength optical lattices in two dimensions for ultracold atoms by using both Guided Modes and Casimir-Polder forces. We further show how to use Guided Modes for photon-induced large and strongly long-range interactions between trapped atoms. Finally, we analyze the prospects of this scheme to implement spin models for quantum simulation
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