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

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.Comment: 19 pages. This vesrion will appear in Mathemetics of Computatio