An Algebraic Framework for Multi-Qudit Computations with Generalized Clifford Algebras

• URL: http://arxiv.org/abs/2103.15324v2
• Date: Mon, 22 Aug 2022 00:40:57 GMT
• Title: An Algebraic Framework for Multi-Qudit Computations with Generalized Clifford Algebras
• Authors: Robert Lin
• Abstract summary: We develop a framework of axioms which abstracts various high-level properties of multi-qudit representations of generalized Clifford algebras. This framework opens the way for developing a graphical calculus for multi-qudit representations of generalized Clifford algebras.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: In this article, we develop an algebraic framework of axioms which abstracts various high-level properties of multi-qudit representations of generalized Clifford algebras. We further construct an explicit model and prove that it satisfies these axioms. Strengths of our algebraic framework include the minimality of its assumptions, and the readiness by which one may give an explicit construction satisfying these assumptions. In terms of applications, this algebraic framework provides a solid foundation which opens the way for developing a graphical calculus for multi-qudit representations of generalized Clifford algebras using purely algebraic methods, which is addressed in a follow-up paper.

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