کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4608647 | 1338369 | 2014 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Estimating the ground state energy of the Schrödinger equation for convex potentials
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 30, Issue 4, August 2014, Pages 469-494
Journal: Journal of Complexity - Volume 30, Issue 4, August 2014, Pages 469-494
نویسندگان
Anargyros Papageorgiou, Iasonas Petras,