2019/12/31 by Kazuhiro Seki, Tomonori Shirakawa, Seiji Yunoki · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Ground state #Hamiltonian (control theory) #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum and electron transport phenomena #Quantum circuit #Quantum error correction #Quantum mechanics #Topology (electrical circuits) #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physreva.101.052340
published as Phys. Rev. A 101, 052340 (2020) · 15 pages, 13 figures, 1 table
openalex publication_date 2020/05/28 · arxiv created 2020/05/29 · arxiv updated 2020/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.