Quantum State Preparation with Resolution Refinement

TL;DR

This paper presents a novel quantum state preparation method called resolution refinement, which iteratively improves eigenstate accuracy by starting from low-resolution states and adiabatically increasing resolution, demonstrating efficiency across various quantum systems.

Contribution

The paper introduces resolution refinement, a new approach for eigenstate preparation on quantum computers that efficiently scales with system size and energy gap.

Findings

Method is efficient across multiple quantum models.

Adiabatic evolution time scales favorably with system parameters.

Resolution refinement does not significantly alter low-energy eigenstates.

Abstract

We introduce a method called resolution refinement that allows one to bootstrap eigenstate preparation on a quantum computer. We first prepare an eigenstate of a low-resolution Hamiltonian using any method of choice. The eigenstate is then lifted to higher resolution and adiabatically evolved to produce the corresponding eigenstate of a higher-fidelity Hamiltonian. We give examples of resolution refinement applied to both single-particle basis states as well as a spatial lattice grid. For basis refinement, we compute few-body ground states of the Busch model for interacting particles in a harmonic trap in one dimension. For lattice refinement, we compute Hartree-Fock nuclear states for a central Woods-Saxon potential in three dimensions, and we compute bound states and continuum states in a multi-species Hubbard model of fermions in one dimension. In all cases, the method is efficient and requires an adiabatic evolution time that scales with the inverse of the energy gap times the square root of the system size. We show that this very favorable scaling arises from the fact that resolution refinement does not make large changes to the structure or energies of the low-energy eigenstates.