A fast algorithm for approximating the ground state energy on a quantum computer
A. Papageorgiou, I. Petras, J. F. Traub, C. Zhang · Mathematics of Computation · 2013
Estimating the ground state energy of a multiparticle system with relative error $\varepsilon$ 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 $\varepsilon$ using a number of qubits $C^\prime d\log \varepsilon ^{-1}$ with total cost (number of queries plus other quantum operations) $Cd\varepsilon ^{-(3+\delta )}$, where $\delta >0$ is arbitrarily small and $C$ and $C^\prime$ are independent of $d$ and $\varepsilon$.