Braiding quantum gates from partition algebras

Abstract

© 2020 Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften. Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the (d, m, l)-generalized Yang-Baxter equation, for m/2 <= l <= m, which allows to systematically construct such braiding operators. This is achieved by using partition algebras, a generalization of the Temperley-Lieb algebra encountered in statistical mechanics. We obtain families of unitary and non-unitary braiding operators that generate the full braid group. Explicit examples are given for a 2-, 3-, and 4-qubit system, including the classification of the entangled states generated by these operators based on Stochastic Local Operations and Classical Communication