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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.03452 |
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| _version_ | 1866910512625745920 |
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| author | van Leeuwen, Robert |
| author_facet | van Leeuwen, Robert |
| contents | We develop a method to deduce the symmetry properties of many-body Hamiltonians when they are prepared in Jordan-Wigner form for evaluation on quantum computers. Symmetries, such as point-group symmetries in molecules, are apparent in the standard second quantized form of the Hamiltonian. They are, however, masked when the Hamiltonian is translated into a Pauli matrix representation required for its operation on qubits. To reveal these symmetries we prove a general theorem that provides a straightforward method to calculate the transformation of Pauli tensor strings under symmetry operations. They are a subgroup of the Clifford group transformations and induce a corresponding group representation inside the symplectic matrices. We finally give a simplified derivation of an affine qubit encoding scheme which allows for the removal of qubits due to Boolean symmetries and thus reduces computational effort in quantum computing applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03452 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revealing symmetries in quantum computing for many-body systems van Leeuwen, Robert Quantum Physics We develop a method to deduce the symmetry properties of many-body Hamiltonians when they are prepared in Jordan-Wigner form for evaluation on quantum computers. Symmetries, such as point-group symmetries in molecules, are apparent in the standard second quantized form of the Hamiltonian. They are, however, masked when the Hamiltonian is translated into a Pauli matrix representation required for its operation on qubits. To reveal these symmetries we prove a general theorem that provides a straightforward method to calculate the transformation of Pauli tensor strings under symmetry operations. They are a subgroup of the Clifford group transformations and induce a corresponding group representation inside the symplectic matrices. We finally give a simplified derivation of an affine qubit encoding scheme which allows for the removal of qubits due to Boolean symmetries and thus reduces computational effort in quantum computing applications. |
| title | Revealing symmetries in quantum computing for many-body systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2407.03452 |