Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation

We propose a quantum-classical hybrid scheme for implementing the nonunitary Gutzwiller factor using discrete Hubbard-Stratonovich transformation, which allows us to express as linear combination of unitary operators involving only single-qubit rotations, at cost sum over auxiliary fields. To perform fields, we introduce two approaches that have complementary features. The first approach employs linear-combination-of-unitaries circuit, enables one probabilistically prepare wave function on quantum computer, while second uses importance sampling estimate observables stochastically, similar Monte Carlo method in classical computation. proposed is demonstrated with numerical simulations half-filled Fermi-Hubbard model. Furthermore, real device, demonstrating can reproduce exact ground-state energy two-site model within error bars.