Simple and efficient end-to-end quantum thermal and ground state preparation

Abstract

Quantum computing algorithms for many-body physics, chemistry and materials science typically require the preparation of thermal or ground states for a given Hamiltonian. We propose quantum algorithms based on system-bath interactions to prepare thermal and ground states for a range of physically relevant Hamiltonians. These algorithms require only forward evolution under a system-bath Hamiltonian in which the bath is a single reusable ancilla qubit, making them especially well-suited for early fault-tolerant quantum devices. By carefully designing the bath and interaction Hamiltonians, we prove that the fixed point of the dynamics accurately approximates the desired quantum state. Furthermore, we establish theoretical guarantees on the mixing time, and thereby provide a rigorous justification for the end-to-end efficiency of system-bath interaction models in thermal and ground state preparation for the physically relevant models we consider.