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Jordan-Wigner formalism for arbitrary 2-input 2-output matchgates and their classical simulation
(Rinton PressQuantum Information and Computation, 2015-05-01)
In Valiant's matchgate theory, 2-input 2-output matchgates are 4 4 matrices that
satisfy ten so-called matchgate identities. We prove that the set of all such matchgates
(including non-unitary and non-invertible ones) ...