Symmetry-adapted variational quantum eigensolver
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.
- Publication:
-
Physical Review A
- Pub Date:
- May 2020
- DOI:
- 10.1103/PhysRevA.101.052340
- arXiv:
- arXiv:1912.13146
- Bibcode:
- 2020PhRvA.101e2340S
- Keywords:
-
- Quantum Physics;
- Condensed Matter - Strongly Correlated Electrons
- E-Print:
- 15 pages, 13 figures, 1 table