Filter-enhanced adiabatic quantum computing on a digital quantum processor

Abstract: Eigenstate filters underpin near-optimal quantum algorithms for ground state preparation. Their realization on current quantum computers, however, poses a challenge as the filters are typically represented by deep quantum circuits. Additionally, since the filters are created probabilistically, their circuits need to be rerun many times when the associated success probability is small. Here we describe a strategy to implement a ground-state filter on quantum hardware in the presence of noise by prepending the filter with digitized adiabatic quantum computing. The adiabatically prepared input state increases the success probability of the filter and also reduces its circuit depth requirements. At the same time, the filter enhances the accuracy of the adiabatically prepared ground state. We compare the approach to the purely adiabatic protocol through numerical simulations and experiments on the Quantinuum H1-1 quantum computer. We demonstrate a significant improvement in ground-state accuracies for paradigmatic quantum spin models.