量子参数化复杂性
Quantum Parameterized Complexity
摘要：
参数化复杂性理论是在20世纪90年代发展起来的，以丰富复杂性理论对依赖于一系列参数的问题的分析。在本文中，我们建立了一个量子等价的经典参数化复杂性理论，动机是需要新的工具来分类现实世界中的问题的复杂性。我们介绍了一系列参数化复杂性类的量子类似物，并研究了这些类、其经典对应类和已充分研究的问题之间的关系。这个框架暴露了丰富的分类的复杂性的参数化版本的QMA困难的问题，演示，例如，一个明确的分离之间的量子线路可满足性问题和局部哈密顿问题。
英文摘要：
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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