Quantum simulation of strongly correlated lattice systems using adaptive algorithms and operator tiling

Adaptive variational quantum simulation algorithms have been shown to be highly successful in finding the ground-state properties of small molecules, but their effectiveness and resource efficiency in the context of condensed matter systems has been studied less. We will present an adaptive algorithm to systematically prepare strongly correlated ground states of lattice Hamiltonians on quantum processors. Our approach utilizes ADAPT-VQE, which requires a user-defined operator pool from which trial wavefunctions are constructed dynamically during runtime. The efficiency of the algorithm depends critically on the choice of pool. We will describe a systematic method for constructing pools for problems with lattice structure called operator tiling, and we prove that such pools are capable of exactly representing the target wavefunction for any system size. We demonstrate the technique on the Heisenberg and Fermi-Hubbard models and establish its effectiveness in finding compact representations of the ground states.