Gutzwiller wave function on a digital quantum computer

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 Ansätze on quantum hardware is therefore important to achieve a 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 nonunitary Gutzwiller operator 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⟩ state confirms the operator was applied. Due to its nondeterministic 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.B.M. acknowledges support from the FCT Ph.D. Scholarship No. SFRH/BD/08444/2020. J.F.R. acknowledges financial support from the Spanish Government (Grant No. PID2019-109539GB-C41), and Generalitat Valenciana funding Prometeo 2017/139