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- Bob Coecke, Dusko Pavlovic, Jamie Vicary
- Mathematical Structures in Computer Science
- 2013

We show that an orthogonal basis for a finite-dimensional Hilbert space can be equivalently characterised as a commutative â€ -Frobenius monoid in the category FdHilb, which has finite-dimensionalâ€¦ (More)

- Krzysztof Bar, Aleks Kissinger, Jamie Vicary
- ArXiv
- 2016

This article introduces Globular, an online proof assistant for the formalization and verification of proofs in higher-dimensional category theory. The tool produces graphical visualizations ofâ€¦ (More)

Web services have the potential to radically enhance the ability of researchers to make use of distributed computing resources, but jargon and a plethora of standards make their use almost impossibleâ€¦ (More)

- Jamie Vicary
- 2013 28th Annual ACM/IEEE Symposium on Logic inâ€¦
- 2013

We use a categorical topological semantics to examine the Deutsch-Jozsa, hidden subgroup and single-shot Grover algorithms. This reveals important structures hidden by conventional algebraicâ€¦ (More)

- W. J. Zeng, Jamie Vicary
- QPL
- 2014

structure of unitary oracles for quantum algorithms W. J. Zengâˆ— Jamie Vicaryâˆ—â€ william.zeng@cs.ox.ac.uk jamie.vicary@cs.ox.ac.uk 5 June 2014 Abstract We show that a pair of complementaryâ€¦ (More)

- Jamie Vicary
- 2008

We describe how â€ -Frobenius monoids give the correct categorical description of two kinds of finite-dimensional â€˜quantum algebrasâ€™. We develop the concept of an involution monoid, and use it to showâ€¦ (More)

- Jamie Vicary
- Electr. Notes Theor. Comput. Sci.
- 2011

We develop the concept of an involution monoid, and use it to show that finite-dimensional C*-algebras are the same as special unitary â€ -Frobenius monoids in the category of finite-dimensionalâ€¦ (More)

- Jamie Vicary
- 2007

This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into aâ€¦ (More)

- Benjamin Musto, Jamie Vicary
- Quantum Information & Computation
- 2016

We introduce quantum Latin squares, combinatorial quantum objects which generalize classical Latin squares. We show that quantum Latin squares can be seen as weakened versions of mutually-unbiasedâ€¦ (More)

- Krzysztof Bar, Jamie Vicary
- 2017 32nd Annual ACM/IEEE Symposium on Logic inâ€¦
- 2017

We present new data structures for quasistrict higher categories, in which associativity and unit laws hold strictly. Our approach has low axiomatic complexity compared to traditional algebraicâ€¦ (More)