Quantum and braided ZX calculus*

Author:

Majid ShahnORCID

Abstract

Abstract We apply quantum group methods to quantum computing, starting with the notion of interacting Frobenius Hopf algebras for ZX calculus with noncommutative algebra and noncocommutative coalgebra. We introduce the notion of *-structures in ZX calculus at this algebraic level and construct examples based on the quantum group u q (sl 2) at a root of unity. We provide an abstract formulation of the Hadamard gate related to Hopf algebra self-duality. We then solve the problem of extending the notion of interacting Hopf algebras and ZX calculus to take place in a braided tensor category. In the ribbon case, the Hadamard gate coming from braided self-duality obeys a modular identity. We give the example of b q (sl 2), the self-dual braided version of u q (sl 2).

Publisher

IOP Publishing

Subject

General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics

Reference33 articles.

1. Codouble bosonisation and dual bases of c q [SL 2] and c q [SL 3];Aziz;J. Algebra,2019

2. A hierarchy of topological tensor network states;Buerschaper;J. Math. Phys.,2013

3. Towards a minimal stabilizer ZX-calculus;Backens;Log. Methods Comput. Sci.,2020

4. Interacting Hopf algebras;Bonchi;J. Pure Appl. Algebra,2017

5. Bar categories and star operations;Beggs;Algebras Represent. Theory,2009

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1. Algebraic aspects of boundaries in the Kitaev quantum double model;Journal of Mathematical Physics;2023-10-01

2. Quantum double aspects of surface code models;Journal of Mathematical Physics;2022-04-01

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