Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4608647 | Journal of Complexity | 2014 | 26 Pages |
Abstract
In 2011, the fundamental gap conjecture for Schrödinger operators was proven. This can be used to estimate the ground state energy of the time-independent Schrödinger equation with a convex potential and relative error ε. Classical deterministic algorithms solving this problem have cost exponential in the number of its degrees of freedom d. We show a quantum algorithm, that is based on a perturbation method, for estimating the ground state energy with relative error ε. The cost of the algorithm is polynomial in d and εâ1, while the number of qubits is polynomial in d and logεâ1. In addition, we present an algorithm for preparing a quantum state that overlaps within 1âδ,δâ(0,1), with the ground state eigenvector of the discretized Hamiltonian. This algorithm also approximates the ground state with relative error ε. The cost of the algorithm is polynomial in d, εâ1 and δâ1, while the number of qubits is polynomial in d, logεâ1 and logδâ1.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Anargyros Papageorgiou, Iasonas Petras,