The Sturm-Liouville eigenvalue problem and NP-complete problems in the quantum setting with queries
摘要
We show how a number of NP-complete as well as NP-hard problems can be reduced to the Sturm-Liouville eigenvalue problem in the quantum setting with queries. We consider power queries which are derived from the propagator of a system evolving with a Hamiltonian obtained from the discretization of the Sturm-Liouville operator. We show that the number of power queries as well the number of qubits needed to solve the problems studied in this paper is a low degree polynomial. The implementation of power queries by a polynomial number of elementary quantum gates is an open issue. If this problem is solved positively for the power queries used for the Sturm-Liouville eigenvalue problem then a quantum computer would be a very powerful computation device allowing us to solve NP-complete problems in polynomial time.
引用
@article{arxiv.quant-ph/0504194,
title = {The Sturm-Liouville eigenvalue problem and NP-complete problems in the quantum setting with queries},
author = {A. Papageorgiou and H. Wozniakowski},
journal= {arXiv preprint arXiv:quant-ph/0504194},
year = {2007}
}
备注
18 pages