Braiding quantum gates from partition algebras

• Main Authors: Pramod Padmanabhan, Fumihiko Sugino, Diego Trancanelli
• Format: Article
• Language: English
• Published: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2020-08-01
• Series: Quantum
• Online Access: https://quantum-journal.org/papers/q-2020-08-27-311/pdf/

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 $m/2\leq l \leq m$, 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.