The measurement calculus

Extended Measurement Calculus

The emergence of quantum computation has changed our perspective on many fundamental aspects of computing: the nature of information and how it flows, new algorithmic design strategies and complexity classes and the very structure of computational models. New challenges have been raised in the physical implementation of quantum computers. This chapter is an investigation into the structure, sco...

Simulating the Measurement Calculus by Rewriting

The one-way model of quantum computing [RB01] has recently emerged as one of the most promising approaches to quantum computing. It is relatively straight forward to demonstrate one-way patterns which simulate the standard unitary gates of the more traditional quantum circuit model and hence realise any circuit computation by composing the appropriate gates. In contrast, the opposite translatio...

A Quantum Game Semantics for the Measurement Calculus

In this paper we present a game semantics for a quantum programming language based on a new definition of quantum strategies. The language studied is MCdata, a typed version of the measurement calculus recently introduced by Danos et. al. We give a soundness and adequacy result based on our quantum game semantics. The main contribution is not the semantics of MCdata but rather the development o...

On a measurement-free quantum lambda calculus with classical control

We study a measurement-free, untyped λ-calculus with quantum data and classical control. This work arises from previous proposals by Selinger and Valiron, and Van Tonder. We focus on operational and expressiveness issues, rather than (denotational) semantics. We prove subject reduction and confluence, and a standardisation theorem. Moreover, we prove the computational equivalence of the propose...

- Calculus , Multiplicities and the - Calculus