Generalized Gottesman-Kitaev-Preskill States on a Quantum Torus
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916969235611648 |
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| author | Joseph, Sijo K. Singh, Sudhir |
| author_facet | Joseph, Sijo K. Singh, Sudhir |
| contents | We introduce a novel formulation of a Generalized Gottesman-Kitaev-Preskill (GKP) state that resolves all of its foundational pathologies, such as infinite energy, non-normalizability, and orthogonality. We demonstrate that these issues are artifacts of defining the code on an unbounded phase-space. By considering the compact quantum-phase-space intrinsic to systems like coupled quantum harmonic oscillators, we have obtained a Generalized GKP (GGKP) state that is both exact and physically realizable. This is achieved by applying an obtained Quantum Zak Transform (QZT) to Squeezed Coherent States, which reveals that Riemann-Theta functions are the natural representation of these states on the quantum torus phase-space. This framework not only provides a well-behaved quantum state, but also reveals a deep connection between quantum error correction, non-commutative geometry, and the theory of generalized Theta functions. This opens a new avenue for fault-tolerant photonic quantum computing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18204 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Gottesman-Kitaev-Preskill States on a Quantum Torus Joseph, Sijo K. Singh, Sudhir Quantum Physics We introduce a novel formulation of a Generalized Gottesman-Kitaev-Preskill (GKP) state that resolves all of its foundational pathologies, such as infinite energy, non-normalizability, and orthogonality. We demonstrate that these issues are artifacts of defining the code on an unbounded phase-space. By considering the compact quantum-phase-space intrinsic to systems like coupled quantum harmonic oscillators, we have obtained a Generalized GKP (GGKP) state that is both exact and physically realizable. This is achieved by applying an obtained Quantum Zak Transform (QZT) to Squeezed Coherent States, which reveals that Riemann-Theta functions are the natural representation of these states on the quantum torus phase-space. This framework not only provides a well-behaved quantum state, but also reveals a deep connection between quantum error correction, non-commutative geometry, and the theory of generalized Theta functions. This opens a new avenue for fault-tolerant photonic quantum computing. |
| title | Generalized Gottesman-Kitaev-Preskill States on a Quantum Torus |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.18204 |