We propose the design of a programming language for quantum computing. Traditionally, quantum algorithms are frequently expressed at the hardware level, for instance in terms of the quantum circuit… (More)

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… (More)

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… (More)

The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda calculus for the classical control model, following the first author’s work on… (More)

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 √ 2 , i]. Moreover, we show that one… (More)

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… (More)

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… (More)

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… (More)

The search for a semantics for higher-order quantum computa tion leads naturally to the study of categories of normed cones. In the first part of this paper, we develop the theory of continuous… (More)