A fast algorithm for approximating the ground state energy on a quantum computer

TL;DR

This paper presents a quantum algorithm that efficiently approximates the ground state energy of multiparticle systems, overcoming classical exponential complexity by using a number of qubits and quantum operations that scale polynomially with system size and desired accuracy.

Contribution

The authors introduce a quantum algorithm that significantly reduces the computational cost of estimating ground state energies compared to classical methods, with cost scaling polynomially in system size and accuracy.

Findings

Quantum algorithm achieves relative error with fewer qubits and operations.

Cost scales as $d imes ext{poly}(rac{1}{ ext{error}})$, avoiding exponential growth.

Demonstrates quantum advantage in quantum chemistry simulations.

Abstract

Estimating the ground state energy of a multiparticle system with relative error $\e$ using deterministic classical algorithms has cost that grows exponentially with the number of particles. The problem depends on a number of state variables $d$ that is proportional to the number of particles and suffers from the curse of dimensionality. Quantum computers can vanquish this curse. In particular, we study a ground state eigenvalue problem and exhibit a quantum algorithm that achieves relative error $\e$ using a number of qubits $C^\prime d\log \e^{-1}$ with total cost (number of queries plus other quantum operations) $Cd\e^{-(3+\delta)}$, where $\delta>0$ is arbitrarily small and $C$ and $C^\prime$ are independent of $d$ and $\e$.