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- Peter Selinger
- Mathematical Structures in Computer Science
- 2004

The field of quantum computation suffers from a lack of syntax. In the absence of a convenient programming language, algorithms are frequently expressed in terms of hardware circuits or Turing machines. Neither approach particularly encourages structured programming or abstractions such as data types. In this paper, we describe the syntax and semantics of a… (More)

- Peter Selinger
- Electr. Notes Theor. Comput. Sci.
- 2007

Dagger compact closed categories were recently introduced by Abramsky and Coecke, under the name “strongly compact closed categories”, as an axiomatic framework for quantum mechanics. We present a graphical language for dagger compact closed categories, and sketch a proof of its completeness for equational reasoning. We give a general construction, the CPM… (More)

- Peter Selinger
- Mathematical Structures in Computer Science
- 2001

We give a categorical semantics to the call-by-name and call-by-value versions of Parigot’s -calculus with disjunction types. We introduce the class of control categories, which combine a cartesian-closed structure with a premonoidal structure in the sense of Power and Robinson. We prove, via a categorical structure theorem, that the categorical semantics… (More)

- Peter Selinger
- 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 to physicists, computer scientists, and others who use diagrammatic reasoning. We have opted for a somewhat informal treatment of topological notions, and have… (More)

- Peter Selinger, Benoît Valiron
- Mathematical Structures in Computer Science
- 2005

In this paper, we develop a functional programming language for quantum computers, by extending the simply-typed lambda calculus with quantum types and operations. The design of this language adheres to the “quantum data, classical control” paradigm, following the first author’s work on quantum flow-charts. We define a call-by-value operational semantics,… (More)

The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing Quipper, a scalable, expressive, functional, higher-order quantum programming language. Quipper has been used to… (More)

- Peter Selinger
- 2003

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 algebraic description of its contours, typically in the form of Bezier curves. The advantage of representing an image as a vector outline is that it can be scaled to… (More)

- Peter Selinger
- Quantum Information & Computation
- 2015

We give an efficient randomized algorithm for approximating an arbitrary element of SU(2) by a product of Clifford+T operators, up to any given error threshold ε > 0. Under a mild hypothesis on the distribution of primes, the algorithm’s expected runtime is polynomial in log(1/ε). If the operator to be approximated is a z-rotation, the resulting gate… (More)

- Peter Selinger
- 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 cones, and prove some of their basic properties, including a Hahn-Banach style theorem. We then describe two different concrete ∗-autonomous categories of… (More)

- Peter Selinger
- Theor. Comput. Sci.
- 2003

Many familiar models of the untyped lambda calculus are constructed by order theoretic methods. This paper provides some basic new facts about ordered models of the lambda calculus. We show that in any partially ordered model that is complete for the theory of βor βη-conversion, the partial order is trivial on term denotations. Equivalently, the open and… (More)