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QMAcomplete problems
, 2012
"... In this paper we give an overview of the quantum computational complexity class QMA and a description of known QMAcomplete problems to date 1. Such problems are believed to be difficult to solve, even with a quantum computer, but have the property that if a purported solution to the problem is give ..."
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In this paper we give an overview of the quantum computational complexity class QMA and a description of known QMAcomplete problems to date 1. Such problems are believed to be difficult to solve, even with a quantum computer, but have the property that if a purported solution to the problem is given, a quantum computer would easily be able to verify whether it is correct. An attempt has been made to make this paper as selfcontained as possible so that it can be accessible to computer scientists, physicists, mathematicians, and quantum chemists. Problems of interest to all of these professions can be found here.
Testing quantum expanders is coQMAcomplete
, 2012
"... A quantum expander is a unital quantum channel that is rapidly mixing, has only a few Kraus operators, and can be implemented efficiently on a quantum computer. We consider the problem of estimating the mixing time (i.e., the spectral gap) of a quantum expander. We show that this problem is coQMAc ..."
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A quantum expander is a unital quantum channel that is rapidly mixing, has only a few Kraus operators, and can be implemented efficiently on a quantum computer. We consider the problem of estimating the mixing time (i.e., the spectral gap) of a quantum expander. We show that this problem is coQMAcomplete. This has applications to testing randomized constructions of quantum expanders, and studying thermalization of open quantum systems. 1