Efficient Preparation of Gutzwiller Ansatz on Noisy Intermediate-Scale Quantum Computers

Digital quantum computers are expected to solve instances of the quantum many-body problem that are intractable in classical hardware, notably those involving strongly-correlated electrons. The leading algorithm in Noisy Intermediate-Scale Quantum Computers (NISQCs) is the Variational Quantum Eigensolver, which attempts to find the ground state by minimizing the energy of a parameterized trial state. This ansatz is typically constructed by initializing a mean-field state, followed by either applying single- and double-electron excitations on this initial state or evolving it via a parameterized multi-step propagator in a similar spirit to adiabatic state preparation. However, as the system size increases, the mean-field state becomes an increasingly worse starting point due to the orthogonality catastrophe. Preparing a more educated guess of the exact ground state is therefore relevant to ease the classical optimization problem. To this end, we discuss how to efficiently prepare on a NISQC the Gutzwiller wavefunction, a simple, yet effective ansatz to approximate the ground state of the Fermi-Hubbard model, the reference model to describe correlated electrons in condensed matter.