Symmetry-adapted variational quantum eigensolver

• URL: http://arxiv.org/abs/1912.13146v2
• Date: Fri, 29 May 2020 08:13:41 GMT
• Title: Symmetry-adapted variational quantum eigensolver
• Authors: Kazuhiro Seki, Tomonori Shirakawa, Seiji Yunoki
• Abstract summary: We propose a scheme to restore spatial symmetry of Hamiltonian in the variational-quantum-eigensolver (VQE) algorithm. The symmetry-adapted VQE scheme simply applies the projection operator, which is Hermitian but not unitary, to restore the spatial symmetry.
• Score: 0.7734726150561086
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a scheme to restore spatial symmetry of Hamiltonian in the variational-quantum-eigensolver (VQE) algorithm for which the quantum circuit structures used usually break the Hamiltonian symmetry. The symmetry-adapted VQE scheme introduced here simply applies the projection operator, which is Hermitian but not unitary, to restore the spatial symmetry in a desired irreducible representation of the spatial group. The entanglement of a quantum state is still represented in a quantum circuit but the nonunitarity of the projection operator is treated classically as postprocessing in the VQE framework. By numerical simulations for a spin-$1/2$ Heisenberg model on a one-dimensional ring, we demonstrate that the symmetry-adapted VQE scheme with a shallower quantum circuit can achieve significant improvement in terms of the fidelity of the ground state and has a great advantage in terms of the ground-state energy with decent accuracy, as compared to the non-symmetry-adapted VQE scheme. We also demonstrate that the present scheme can approximate low-lying excited states that can be specified by symmetry sectors, using the same circuit structure for the ground-state calculation.

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