Symmetryadapted variational quantum eigensolver
Abstract
We propose a scheme to restore spatial symmetry of Hamiltonian in the variationalquantumeigensolver (VQE) algorithm for which the quantum circuit structures used usually break the Hamiltonian symmetry. The symmetryadapted 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 spin1 /2 Heisenberg model on a onedimensional ring, we demonstrate that the symmetryadapted 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 groundstate energy with decent accuracy, as compared to the nonsymmetryadapted VQE scheme. We also demonstrate that the present scheme can approximate lowlying excited states that can be specified by symmetry sectors, using the same circuit structure for the groundstate 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
 EPrint:
 15 pages, 13 figures, 1 table