2013/09/25 by Anargyros Papageorgiou, Papageorgiou, Anargyros, Iasonas Petras +1 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1309.6578
arxiv created 2013/09/25 · openalex publication_date 2013/09/25 · arxiv updated 2013/09/26 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
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 ε-1, while the number of qubits is polynomial in d and logε-1. In addition, we present an algorithm for preparing a quantum state that overlaps within 1-δ, δ∈ (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, ε-1 and δ-1, while the number of qubits is polynomial in d, logε-1 and logδ-1.