Quantum Merlin Arthur (QMA) is a complexity class in quantum computing. It is a quantum analogue of the classical complexity class NP (nondeterministic polynomial time).
In classical computing, the class NP includes decision problems that can be verified in polynomial time. For example, if an answer to a problem can be guessed in polynomial time, it can then be checked in polynomial time as well. In quantum computing, decision problems that can be verified in polynomial time using a quantum computer belong to the QMA complexity class.
QMA was introduced by John Watrous in 2000 as a generalization of the class QCMA (Quantum Class Merlin Arthur) introduced by Dorit Aharonov, et al. QMA allows for quantum verifiers to provide quantum proofs to quantum polynomial time machines (Merlin) about the validity of a problem instance.
QMA is considered a fundamental complexity class in quantum computing, and its study helps to understand the power and limitations of quantum computers. The aim is to understand how much advantage quantum computers can provide over classical ones in terms of solving computational problems.
Due to its theoretical nature, QMA has not yet found significant practical applications. However, its study is important in the broader context of quantum complexity theory and the development of quantum algorithms.
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