Braiding quantum gates from partition algebras
Abstract
Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solutiongenerating technique to solve the (d,m,l)generalized YangBaxter 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 TemperleyLieb algebra encountered in statistical mechanics. We obtain families of unitary and nonunitary braiding operators that generate the full braid group. Explicit examples are given for a 2, 3, and 4qubit system, including the classification of the entangled states generated by these operators based on Stochastic Local Operations and Classical Communication.
 Publication:

Quantum
 Pub Date:
 August 2020
 DOI:
 10.22331/q20200827311
 arXiv:
 arXiv:2003.00244
 Bibcode:
 2020Quant...4..311P
 Keywords:

 Quantum Physics;
 High Energy Physics  Theory;
 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 38 pages, 8 figures