Adiabatic state preparation from general initial states

TL;DR

This paper introduces a heuristic method for adiabatic state preparation that starts from a general initial wavefunction, improving ground state approximations in quantum computing by constructing an adiabatic path tailored to the initial state.

Contribution

The paper presents a novel algorithm to construct adiabatic paths from arbitrary initial states, including a way to approximate parent Hamiltonians and verify their quality beforehand.

Findings

Successfully simulated water ground state using the method.

Effectively prepared multireference state of methylene.

Demonstrated flexibility with various initial wavefunctions.

Abstract

A variety of quantum computing algorithms exist for the preparation of approximate Hamiltonian ground states. A natural and important question is how these ground-state approximations can be further improved using adiabatic state preparation. Here, we present a heuristic method to carry out adiabatic state preparation starting from a generic initial wavefunction. Given a quantum circuit that prepares the initial wavefunction, and a target Hamiltonian for which one wishes to prepare the ground state, we present an algorithm to construct an adiabatic path between these two states. This method works by approximating a parent Hamiltonian for the initial wavefunction, and the quality of this approximation can be can be checked prior to running the ASP algorithm. We apply this technique to simulate the ground state of water and the lowest-lying multireference singlet state of methylene, using various initial wavefunctions as the starting point of the adiabatic path.