Parameterized Complexity of Weighted Local Hamiltonian Problems and the Quantum Exponential Time Hypothesis
Computational Complexity
2022-11-11 v1 Quantum Physics
Abstract
We study a parameterized version of the local Hamiltonian problem, called the weighted local Hamiltonian problem, where the relevant quantum states are superpositions of computational basis states of Hamming weight . The Hamming weight constraint can have a physical interpretation as a constraint on the number of excitations allowed or particle number in a system. We prove that this problem is in QW[1], the first level of the quantum weft hierarchy and that it is hard for QM[1], the quantum analogue of M[1]. Our results show that this problem cannot be fixed-parameter quantum tractable (FPQT) unless certain natural quantum analogue of the exponential time hypothesis (ETH) is false.
Cite
@article{arxiv.2211.05325,
title = {Parameterized Complexity of Weighted Local Hamiltonian Problems and the Quantum Exponential Time Hypothesis},
author = {Michael J. Bremner and Zhengfeng Ji and Xingjian Li and Luke Mathieson and Mauro E. S. Morales},
journal= {arXiv preprint arXiv:2211.05325},
year = {2022}
}
Comments
37 pages, 10 figures