2017/05/02 by Arash Pourkia, Pourkia, Arash
Mathematics · Computer Science · #Algebraic structures and combinatorial models #Quantum Information and Cryptography #Quantum Computing Algorithms and Architecture
paper · pdf · doi:10.48550/arxiv.1705.00940
Many well-known and well-studied four by four universal quantum logic gates in the literature are of a specific form, the so called eight-vertex form \eqref8vertexform \citekaufman etal 05-1,kaufman etal 05-2, or \it similar to it. We present a formalism for universal quantum logic gates of such a form. First, we provide explicit formulas in terms of matrix entries, which are the necessary and sufficient conditions for such a matrix to be a solution to the Yang-Baxter equation \eqrefbyb. Then, combining this with the conditions needed for being unitary \eqrefunitarycond and being entangling \eqrefentanglingcond, we give a full description of entangling unitary solutions to the Yang-Baxter equation (hence, universal quantum logic gates) of such a specific form. We investigate in detail all the possible cases where some of the eight main entries might or might not be zero.