Improved Techniques for Preparing Eigenstates of Fermionic Hamiltonians

TL;DR

This paper introduces three advanced quantum algorithms to efficiently prepare eigenstates of fermionic Hamiltonians, significantly reducing computational costs and errors in quantum simulations of chemical and material systems.

Contribution

The paper presents a polylogarithmic-depth antisymmetrization algorithm, a method to reduce repeated state preparation overhead, and an exact zero-error time evolution technique using qubitization.

Findings

Polylogarithmic-depth antisymmetrization algorithm developed.

Reduced overhead in phase estimation for ground state preparation.

Exact zero-error time evolution via qubitization demonstrated.

Abstract

Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost of preparing fermionic Hamiltonian eigenstates using phase estimation. First, we report a polylogarithmic-depth quantum algorithm for antisymmetrizing the initial states required for simulation of fermions in first quantization. This is an exponential improvement over the previous state-of-the-art. Next, we show how to reduce the overhead due to repeated state preparation in phase estimation when the goal is to prepare the ground state to high precision and one has knowledge of an upper bound on the ground state energy that is less than the excited state energy (often the case in quantum chemistry). Finally, we explain how one can perform the time evolution necessary for the phase estimation based preparation of Hamiltonian eigenstates with exactly zero error by using the recently introduced qubitization procedure.