Variational quantum eigensolver with fewer qubits

• DOI: 10.1103/physrevresearch.1.023025
• Publication Date: 2019-09-24T12:11:11Z
• Authors: Jin-Guo Liu; Yi-Hong Zhang; Yuan Wan; Lei Wang
• Keywords: Quantum Physics; Condensed Matter - Strongly Correlated Electrons; Strongly Correlated Electrons (cond-mat.str-el); Physics; QC1-999; 0103 physical sciences; FOS: Physical sciences; Quantum Physics (quant-ph); 01 natural sciences

We propose a qubit efficient scheme to study ground state properties of quantum many-body systems on near-term noisy intermediate scale computers. One can obtain tensor network representation the using number qubits smaller than physical degrees freedom. By increasing number, one exponentially increase bond dimension variational ansatz computer. Moreover, we construct circuits blocks which respect U(1) and SU(2) symmetries system show that they significantly speed up training process alleviate gradient vanishing problem. To demonstrate feasibility eigensolver in practical setting, perform first principle classical simulation differentiable programming circuits. Using only $6$ $4\times 4$ square lattice frustrated Heisenberg model with fidelity over 97%. Arbitrarily long ranged correlations also be measured same circuit after optimization.