Representing Matrices Using Algebraic ZX-calculus

This work is an important addition to the body of literature on formal graphical languages. The graphical language in question is the algebraic ZX calculus, which is purely formulated in terms of string diagrams and is universal for linear maps. Here, an efficient method is defined to represent any given matrix as a string diagram. The algebraic ZX calculus is also complete for linear maps, meaning that any equation proven via linear algebra can also be proven via diagrammatic manipulations. Thus, one can study the structure of matrices that play an important role in condensed matter physics, machine learning, and other applications of interest, by representing matrices and tensors as string diagrams in the algebraic ZX calculus.

Quanlong Wang

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