• Publications
  • Influence
Dagger Compact Closed Categories and Completely Positive Maps: (Extended Abstract)
  • P. Selinger
  • Computer Science, Mathematics
    Electron. Notes Theor. Comput. Sci.
  • 1 March 2007
This work presents a graphical language for dagger compact closed categories, and sketches a proof of its completeness for equational reasoning, and gives a general construction, the CPM construction, which associates to each Dagger compact closed category its ''category of completely positive maps'', and shows that the resulting category is again dagger compactclosed.
Towards a quantum programming language
  • P. Selinger
  • Computer Science
    Mathematical Structures in Computer Science
  • 1 August 2004
This paper describes the syntax and semantics of a simple quantum programming language with high-level features such as loops, recursive procedures, and structured data types, and has an interesting denotational semantics in terms of complete partial orders of superoperators.
A Survey of Graphical Languages for Monoidal Categories
This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also
Quipper: a scalable quantum programming language
Quipper, a scalable, expressive, functional, higher-order quantum programming language, which is geared towards a model of computation that uses a classical computer to control a quantum device, but is not dependent on any particular model of quantum hardware.
Control categories and duality: on the categorical semantics of the lambda-mu calculus
  • P. Selinger
  • Mathematics, Computer Science
    Mathematical Structures in Computer Science
  • 30 March 2001
It is proved, via a categorical structure theorem, that the categorical semantics is equivalent to a CPS semantics in the style of Hofmann and Streicher, and that the call-by-name λμ-calculus forms an internal language for the dual co-control categories.
Potrace : a polygon-based tracing algorithm
Black-on-white images can be represented either as a bitmap or as a vector outline. A bitmap represents an image as a grid of black or white pixels. A vector outline describes an image via an
Exact synthesis of multi-qubit Clifford+T circuits
We prove that a unitary matrix has an exact representation over the Clifford+$T$ gate set with local ancillas if and only if its entries are in the ring $\mathbb{Z}[\frac{1}{\sqrt{2}},i]$. Moreover,
Towards a semantics for higher-order quantum computation
The search for a semantics for higher-order quantum computation leads naturally to the study of categories of normed cones. In the first part of this paper, we develop the theory of continuous normed
A Lambda Calculus for Quantum Computation with Classical Control
The main results of this paper are the safety properties of the language and the development of a type inference algorithm.
Quantum circuits of T-depth one
  • P. Selinger
  • Physics, Computer Science
  • 2 October 2012
A class of circuits whose T- depth can be reduced to 1 by using sufficiently many ancillas is described, and it is shown that the cost of adding an additional control to any controlled gate is at most 8 additional T-gates, and T-depth 2.