Categorical quantum circuits
Ville Bergholm, Jacob Biamonte · Journal of Physics A Mathematical and Theoretical · 2011
In this paper, we extend previous work carried out on the application of the mathematics of category theory to quantum information science.Specifically, we present a realization of a dagger-compact category that can model finitedimensional quantum systems and explicitly allows for the interaction of systems of arbitrary, possibly unequal, dimensions.Hence, our framework can handle generic tensor network states, including matrix product states.Our categorical model subsumes the traditional quantum circuit model while remaining directly and easily applicable to problems stated in the language of quantum information science.The circuit diagrams themselves now become morphisms in a category, making quantum circuits a special case of a much more general mathematical framework.We introduce the key algebraic properties of our tensor calculus diagrammatically and show how they can be applied to solve problems in the field of quantum information.