Quantum Parameterized Complexity
Abstract
Parameterized complexity theory was developed in the 1990s to enrich the complexity-theoretic analysis of problems that depend on a range of parameters. In this paper we establish a quantum equivalent of classical parameterized complexity theory, motivated by the need for new tools for the classifications of the complexity of real-world problems. We introduce the quantum analogues of a range of parameterized complexity classes and examine the relationship between these classes, their classical counterparts, and well-studied problems. This framework exposes a rich classification of the complexity of parameterized versions of QMA-hard problems, demonstrating, for example, a clear separation between the Quantum Circuit Satisfiability problem and the Local Hamiltonian problem.
Cite
@article{arxiv.2203.08002,
title = {Quantum Parameterized Complexity},
author = {Michael J. Bremner and Zhengfeng Ji and Ryan L. Mann and Luke Mathieson and Mauro E. S. Morales and Alexis T. E. Shaw},
journal= {arXiv preprint arXiv:2203.08002},
year = {2022}
}
Comments
23 pages, 1 figure