Quantum Discrete Variable Representations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915253400371200 |
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| author | Pliś, Szymon Zak, Emil |
| author_facet | Pliś, Szymon Zak, Emil |
| contents | We present a fault-tolerant quantum algorithm for implementing the Discrete Variable Representation (DVR) transformation, a technique widely used in simulations of quantum-mechanical Hamiltonians. DVR provides a diagonal representation of local operators and enables sparse Hamiltonian structures, making it a powerful alternative to the finite basis representation (FBR), particularly in high-dimensional problems. While DVR has been extensively used in classical simulations, its quantum implementation, particularly using Gaussian quadrature grids, remains underexplored. We develop a quantum circuit that efficiently transforms FBR into DVR by following a recursive construction based on quantum arithmetic operations, and we compare this approach with methods that directly load DVR matrix elements using quantum read-only memory (QROM). We analyze the quantum resources, including T-gate and qubit counts, required for implementing the DVR unitary and discuss preferable choices of QROM-based and recursive-based methods for a given matrix size and precision. This study lays the groundwork for utilizing DVR Hamiltonians in quantum algorithms such as quantum phase estimation with block encoding. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15841 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Discrete Variable Representations Pliś, Szymon Zak, Emil Quantum Physics Chemical Physics Computational Physics 68Q12, 68Q17, 81P68, 81-08, 81-10, 81V74, 81V55 G.1.2; G.1.3; G.1.6; I.6.1 We present a fault-tolerant quantum algorithm for implementing the Discrete Variable Representation (DVR) transformation, a technique widely used in simulations of quantum-mechanical Hamiltonians. DVR provides a diagonal representation of local operators and enables sparse Hamiltonian structures, making it a powerful alternative to the finite basis representation (FBR), particularly in high-dimensional problems. While DVR has been extensively used in classical simulations, its quantum implementation, particularly using Gaussian quadrature grids, remains underexplored. We develop a quantum circuit that efficiently transforms FBR into DVR by following a recursive construction based on quantum arithmetic operations, and we compare this approach with methods that directly load DVR matrix elements using quantum read-only memory (QROM). We analyze the quantum resources, including T-gate and qubit counts, required for implementing the DVR unitary and discuss preferable choices of QROM-based and recursive-based methods for a given matrix size and precision. This study lays the groundwork for utilizing DVR Hamiltonians in quantum algorithms such as quantum phase estimation with block encoding. |
| title | Quantum Discrete Variable Representations |
| topic | Quantum Physics Chemical Physics Computational Physics 68Q12, 68Q17, 81P68, 81-08, 81-10, 81V74, 81V55 G.1.2; G.1.3; G.1.6; I.6.1 |
| url | https://arxiv.org/abs/2504.15841 |