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arXiv · 2203.08002

Quantum Parameterized Complexity

Michael J. Bremner·Zhengfeng Ji·Ryan L. Mann·Luke Mathieson·Mauro E. S. Morales·Alexis T. E. Shaw
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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.

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Michael J. Bremner, Zhengfeng Ji, Ryan L. Mann, Luke Mathieson, Mauro E. S. Morales, Alexis T. E. Shaw. 2022-03-15. Quantum Parameterized Complexity. https://arxiv.org/abs/2203.08002

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