Concept

QMA

Summary
In computational complexity theory, QMA, which stands for Quantum Merlin Arthur, is the set of languages for which, when a string is in the language, there is a polynomial-size quantum proof (a quantum state) that convinces a polynomial time quantum verifier (running on a quantum computer) of this fact with high probability. Moreover, when the string is not in the language, every polynomial-size quantum state is rejected by the verifier with high probability. The relationship between QMA and BQP is analogous to the relationship between complexity classes NP and P. It is also analogous to the relationship between the probabilistic complexity class MA and BPP. QAM is a related complexity class, in which fictional agents Arthur and Merlin carry out the sequence: Arthur generates a random string, Merlin answers with a quantum certificate and Arthur verifies it as a BQP machine. Definition A language L is in \mathsf{QMA}(c,s) if there exists a polynomial time q
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