The Harrow-Hassidim-Lloyd algorithm with qutrits
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912940870860800 |
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| author | Patel, Tushti Prasannaa, V. S. |
| author_facet | Patel, Tushti Prasannaa, V. S. |
| contents | We extend the Harrow-Hassidim-Lloyd (HHL) algorithm, which is well-studied in the qubit framework, to its qutrit counterpart (which we call qutrit HHL, as opposed to qubit HHL, which is HHL using qubits), and develop a program for its implementation. We design Weyl-Heisenberg gadgets, the qutrit equivalents of Pauli gadgets, and come up with a practical implementation scheme for qutrit HHL. We test HHL with qutrits for simple matrices and verify the results against the expected outcomes. We apply the algorithm to quantum chemistry, and in particular, to the potential energy curve calculations of the model problem of the Hydrogen molecule in the split valence basis. We do so for two cases: 1-qutrit and 2-qutrit input states, where the latter makes use of our gadgets. We compare the number of qudits and the number of gates required between qubit and qutrit HHL implementations. In general, we find that for a fixed precision, the qutrit HHL circuit requires fewer number of qudits and comparable number of two-qudit gates than its qubit counterpart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17960 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Harrow-Hassidim-Lloyd algorithm with qutrits Patel, Tushti Prasannaa, V. S. Quantum Physics Atomic Physics Chemical Physics We extend the Harrow-Hassidim-Lloyd (HHL) algorithm, which is well-studied in the qubit framework, to its qutrit counterpart (which we call qutrit HHL, as opposed to qubit HHL, which is HHL using qubits), and develop a program for its implementation. We design Weyl-Heisenberg gadgets, the qutrit equivalents of Pauli gadgets, and come up with a practical implementation scheme for qutrit HHL. We test HHL with qutrits for simple matrices and verify the results against the expected outcomes. We apply the algorithm to quantum chemistry, and in particular, to the potential energy curve calculations of the model problem of the Hydrogen molecule in the split valence basis. We do so for two cases: 1-qutrit and 2-qutrit input states, where the latter makes use of our gadgets. We compare the number of qudits and the number of gates required between qubit and qutrit HHL implementations. In general, we find that for a fixed precision, the qutrit HHL circuit requires fewer number of qudits and comparable number of two-qudit gates than its qubit counterpart. |
| title | The Harrow-Hassidim-Lloyd algorithm with qutrits |
| topic | Quantum Physics Atomic Physics Chemical Physics |
| url | https://arxiv.org/abs/2511.17960 |