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

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'd log e^-1 with total cost (number of queries plus other quantum operations) Cde^-(3+d), where d > 0 is arbitrarily small and C and C' are independent of d and e.