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arXiv · 2003.00244

Braiding quantum gates from partition algebras

Pramod Padmanabhan·Fumihiko Sugino·Diego Trancanelli
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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 $m/2\leq l \leq m$, 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.

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quant-phhep-thmath-phmath.MPnlin.SI

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BibTeXRIS

Pramod Padmanabhan, Fumihiko Sugino, Diego Trancanelli. 2020-02-29. Braiding quantum gates from partition algebras. https://doi.org/10.22331/q-2020-08-27-311

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