OASIS - Philippe Jorrand

The Oxford Advanced Seminar on Informatic Structures

$\*$ Introduction to OASIS

$\*$ Michaelmas 2004

$\*$ Hilary 2005

$\*$ Trinity 2005

$\*$ Simon Gay

$\*$ Dov Gabbay

$\*$ Philippe Jorrand

$\*$ Michael Fellows

$\*$ Mai Gehrke

$\*$ Michaelmas 2005

$\*$ Hilary 2006

$\*$ Trinity 2006

$\*$ Michaelmas 2006

$\*$ Hilary 2007

$\*$ Trinity 2007

$\*$ Michaelmas 2007

$\*$ Hilary 2008

$\*$ Trinity 2008

Philippe Jorrand

[Leibniz Laboratory - Grenoble - France]

TITLE: The complexity of graph state preparation (joint work with Mehdi Mhalla and Simon Perdrix)

ABSTRACT: Graph states are entangled quantum states described by means of mathematical graphs. They are useful in some purification schemes and, most importantly, they adequately represent the entangled states consumed by measurement-based quantum computations. This talk will deal with the complexity of preparing a graph state, given the graph describing it. Three kinds of resources may be used during a graph state preparation: (i) some number of ancillary qubits, (ii) unitary operators and/or measurement observables of some maximal size (i.e. the maximum number of qubits operated upon by one operation), and (iii), some time (i.e. the number of successive steps needed to reach the target state). Each order of priority among these three parameters defines a measure of complexity. For each measure, upper and lower bounds of the complexity of graph state preparation will be defined, with a special focus on the case of graph state preparation my means of quantum measurements only (i.e. without applying any unitary operator).

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