Gutzwiller wave function on a digital quantum computer

TL;DR

This paper introduces a quantum algorithm to efficiently prepare the Gutzwiller Wave Function for simulating the Fermi-Hubbard model, enabling better initialization of quantum states for correlated electron systems.

Contribution

It presents a novel quantum routine for initializing the Gutzwiller Wave Function, including a measurement-based projection method with analysis of success rates and circuit scaling.

Findings

Successful preparation of GWF on quantum hardware demonstrated

Success probability depends on lattice size and interaction strength

Circuit metrics scale with system size and interaction parameters

Abstract

The determination of the ground state of quantum many-body systems via digital quantum computers rests upon the initialization of a sufficiently educated guess. This requirement becomes more stringent the greater the system. Preparing physically-motivated ans\"{a}tze on quantum hardware is therefore important to achieve quantum advantage in the simulation of correlated electrons. In this spirit, we introduce the Gutzwiller Wave Function (GWF) within the context of the digital quantum simulation of the Fermi-Hubbard model. We present a quantum routine to initialize the GWF that comprises two parts. In the first, the noninteracting state associated with the $U = 0$ limit of the model is prepared. In the second, the non-unitary Gutzwiller projection that selectively removes states with doubly-occupied sites from the wave function is performed by adding to every lattice site an ancilla qubit, the measurement of which in the $|0\rangle$ state confirms the projection was made. Due to its non-deterministic nature, we estimate the success rate of the algorithm in generating the GWF as a function of the lattice size and the interaction strength $U/t$. The scaling of the quantum circuit metrics and its integration in general quantum simulation algorithms are also discussed.