An Introduction to One-Way Patterns

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The one-way measurement model is a model of quantum computation which is intriguing for its' potential as a means of implementing quantum computers, but also for theoretical purposes for the different way in which it allows quantum operations to be described. Instead of a sequence of unitary gates on an array of ``wires'', operations are described in terms of emph{patterns}, consisting of a graph of entanglement relations on a set of qubits, together with a collection of measurement angles for these qubits (except possibly for a subset which will support a final quantum state). In this introductory talk, I describe the relationship between patterns in the one-way measurement model to quantum circuits, and explore patterns which represent unitary operations but which emph{don't} have direct analogues in the circuit model.