Weyl's Relations, Integrable Matrix Models and Quantum Computation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915863533191168 |
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| author | Shastry, B. Sriram Yuzbashyan, Emil A. Patra, Aniket |
| author_facet | Shastry, B. Sriram Yuzbashyan, Emil A. Patra, Aniket |
| contents | Starting from a generalization of Weyl's relations in finite dimension $N$, we show that the Heisenberg commutation relations can be satisfied in a specific $N-1$ dimensional subspace, and display a linear map for projecting operators to this subspace. This setup is used to construct a hierarchy of parameter-dependent commuting matrices in $N$ dimensions. This family of commuting matrices is then related to Type-1 matrices representing quantum integrable models. The commuting matrices find an interesting application in quantum computation, specifically in Grover's database search problem. Each member of the hierarchy serves as a candidate Hamiltonian for quantum adiabatic evolution and, in some cases, achieves higher fidelity than standard choices -- thus offering improved performance. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_16841 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weyl's Relations, Integrable Matrix Models and Quantum Computation Shastry, B. Sriram Yuzbashyan, Emil A. Patra, Aniket Quantum Physics Statistical Mechanics Mathematical Physics Starting from a generalization of Weyl's relations in finite dimension $N$, we show that the Heisenberg commutation relations can be satisfied in a specific $N-1$ dimensional subspace, and display a linear map for projecting operators to this subspace. This setup is used to construct a hierarchy of parameter-dependent commuting matrices in $N$ dimensions. This family of commuting matrices is then related to Type-1 matrices representing quantum integrable models. The commuting matrices find an interesting application in quantum computation, specifically in Grover's database search problem. Each member of the hierarchy serves as a candidate Hamiltonian for quantum adiabatic evolution and, in some cases, achieves higher fidelity than standard choices -- thus offering improved performance. |
| title | Weyl's Relations, Integrable Matrix Models and Quantum Computation |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2506.16841 |