Jordan-Wigner formalism for arbitrary 2-input 2-output matchgates and their classical simulation

Richard Jozsa, Akimasa Miyake, Sergii Strelchuk

In Valiant's matchgate theory, 2-input 2-output matchgates are 4x4 matrices that satisfy ten so-called matchgate identities. We prove that the set of all such matchgates (including…