Accessing ground-state and excited-state energies in a many-body system after symmetry restoration using quantum computers

Abstract

We explore the possibility to perform symmetry restoration with the variation after projection technique on a quantum computer followed by additional postprocessing. The final goal is to develop configuration interaction techniques based on many-body trial states preoptimized on a quantum computer. We show how the projection method used for symmetry restoration can prepare optimized states that could then be employed as initial states for quantum or hybrid quantum-classical algorithms. We use the quantum phase estimation and the quantum Krylov approaches for the postprocessing. The latter method combined with the quantum variation after projection leads to very fast convergence toward the ground-state energy. The possibility to access excited states energies is also discussed. Illustrations of the different techniques are made using the pairing Hamiltonian.