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Horizons of the Mind. A Tribute to Prakash Panangaden pp 427–453Cite as

Entanglement, Flow and Classical Simulatability in Measurement Based Quantum Computation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8464))

Abstract

The question of which and how a particular class of entangled resource states (known as graph states) can be used for measurement based quantum computation (MBQC) recently gave rise to the notion of Flow and its generalisation gFlow. That is a causal structure for measurements guaranteeing deterministic computation. Furthermore, gFlow has proven itself to be a powerful tool in studying the difference between the measurement-based and circuit models for quantum computing, as well as analysing cryptographic protocols. On the other hand, entanglement is known to play a crucial role in MBQC. In this paper we first show how gFlow can be used to directly give a bound on the classical simulation of an MBQC. Our method offers an interpretation of the gFlow as showing how information flows through a computation, giving rise to an information light cone.We then establish a link between entanglement and the existence of gFlow for a graph state. We show that the gFlow can be used to upper bound the entanglement width and what we call the structural entanglement of a graph state. In turn this gives another method relating the gFlow to upper bound on how efficiently a computation can be simulated classically. These two methods of getting bounds on the difficulty of classical simulation are different and complementary and several known results follow. In particular known relations between the MBQC and the circuit model allow these results to be translated across models.

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Author information

Authors and Affiliations

  1. CNRS LTCI, Département Informatique et Réseaux, Telecom ParisTech, 23 avenue d’Italie, CS, 51327, 75214, Paris CEDEX 13, France

    Damian Markham

  2. School of Informatics, University of Edinburgh, 10 Crichton Street, Edinburgh, EH8 9AB, UK

    Elham Kashefi

Authors
  1. Damian Markham
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  2. Elham Kashefi
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, York University, Keele Street, 4700, M3J 1P3, Toronto, ON, Canada

    Franck van Breugel

  2. School of Informatics, Informatics Forum, University of Edinburgh, 10 Crichton Street, EH8 9LE, Edinburgh, UK

    Elham Kashefi

  3. Inria Saclay, Campus de l’École Polytechnique, Bâtiment Alan Turing, 1, rue Honoré d’Estienne d’Orves, 91120, Palaiseau, France

    Catuscia Palamidessi

  4. CWI, P.O. Box 94079, 1090, Amsterdam, GB, The Netherlands

    Jan Rutten

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Markham, D., Kashefi, E. (2014). Entanglement, Flow and Classical Simulatability in Measurement Based Quantum Computation. In: van Breugel, F., Kashefi, E., Palamidessi, C., Rutten, J. (eds) Horizons of the Mind. A Tribute to Prakash Panangaden. Lecture Notes in Computer Science, vol 8464. Springer, Cham. https://doi.org/10.1007/978-3-319-06880-0_22

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  • DOI: https://doi.org/10.1007/978-3-319-06880-0_22

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06879-4

  • Online ISBN: 978-3-319-06880-0

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