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- 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)

It differs from the present version in that it has been copy-edited and reformatted. Abstract 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 β-or… (More)

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)

- Peter Selinger
- 2003

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
- 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)

In this paper, we propose an adversary-centric, logical framework for formalizing cryptographic protocols. The formalism is inspired by the work of Compton and Dexter and of Cervesato et al., but we do not focus on proof search, but instead on logical validity. A novel contribution of this paper is a technique for giving very short proofs of protocol… (More)

Overview Given a gate set S universal for quantum computing, the problem of decomposing a unitary operator U into a circuit over S is known as the synthesis problem. This problem can be solved exactly, if U belongs to the set of circuits generated by S. Otherwise, it can be solved approximately, by finding a circuit U such that ||U − U || < for some chosen… (More)

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)