Revealing symmetries in quantum computing for many-body systems

• URL: http://arxiv.org/abs/2407.03452v1
• Date: Wed, 3 Jul 2024 18:53:09 GMT
• Title: Revealing symmetries in quantum computing for many-body systems
• Authors: Robert van Leeuwen,
• Abstract summary: We deduce the symmetry properties of many-body Hamiltonians when they are prepared in Jordan-Wigner form for evaluation on quantum computers. We prove a general theorem that provides a straightforward method to calculate the transformation of Pauli tensor strings under symmetry operations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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