Braiding quantum gates from partition algebras

Abstract

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

arXiv comment38 pages, 8 figures; v2: minor changes, added references; v3: fixed hyperlinks for the references, published version

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Cited by in corpus (8)

• Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras
• Optimal realization of Yang-Baxter gate on quantum computers
• Local invariants of braiding quantum gates -- associated link polynomials and entangling power
• Algebraic classification of Hietarinta's solutions of Yang-Baxter equations~:~invertible $4\times 4$ operators
• Geometric representations of braid and Yang-Baxter gates
• New series of multi-parametric solutions to GYBE: quantum gates and integrability
• Majorana fermions solve the tetrahedron equations as well as higher simplex equations
• Almost local integrable models from supersymmetry algebras