We give a general construction, the CPM construction, which associates to each dagger compact closed category its ''category of completely positive maps'', and a proof of its completeness for equational reasoning.Expand

In this paper, we describe the syntax and semantics of a simple quantum programming language with high-level features such as loops, recursive procedures, and structured data types.Expand

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… Expand

We introduce Quipper, a scalable, expressive, functional, higher-order quantum programming language that can program a diverse set of non-trivial quantum algorithms.Expand

We introduce Quipper, a scalable, expressive, functional, higher-order quantum programming language that can program a diverse set of non-trivial quantum algorithms.Expand

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 Z[1/sqrt(2),i].Expand

We give an efficient randomized algorithm for approximating an arbitrary element of SU(2) by a product of Clifford+T gates, up to arbitrarily small ε.Expand

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… Expand