Dagger Compact Closed Categories and Completely Positive Maps: (Extended Abstract)
- P. Selinger
- MathematicsQPL
- 1 March 2007
Towards a quantum programming language
- P. Selinger
- Computer ScienceMathematical 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
- P. Selinger
- Mathematics
- 23 August 2009
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
- A. S. Green, P. Lumsdaine, Neil J. Ross, P. Selinger, B. Valiron
- Computer Science, PhysicsACM-SIGPLAN Symposium on Programming Language…
- 11 April 2013
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
- Computer ScienceMathematical 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.
Quantum circuits of T-depth one
- P. Selinger
- MathematicsArXiv
- 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.
Exact synthesis of multi-qubit Clifford+T circuits
- Brett Gordon Giles, P. Selinger
- MathematicsArXiv
- 3 December 2012
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,…
Optimal ancilla-free Clifford+T approximation of z-rotations
- Neil J. Ross, P. Selinger
- Computer ScienceQuantum information & computation
- 12 March 2014
We consider the problem of approximating arbitrary single-qubit z-rotations by ancilla-free Clifford+T circuits, up to given epsilon. We present a fast new probabilistic algorithm for solving this…
Potrace : a polygon-based tracing algorithm
- P. Selinger
- Computer Science
- 2003
This paper describes a tracing algorithm, called Potrace, which stands for polygon tracer, which uses polygons as an intermediate representation of images and is designed to work well on high resolution images.
Towards a semantics for higher-order quantum computation
- P. Selinger
- Mathematics
- 2004
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…
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