Categorical quantum circuits

Ville Bergholm, Jacob D. Biamonte

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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 finite-dimensional 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.

Original languageEnglish (US)
Article number245304
JournalJournal of Physics A: Mathematical and Theoretical
Issue number24
StatePublished - Jun 17 2011

All Science Journal Classification (ASJC) codes

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


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