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Entanglement, Flow and Classical Simulatability in Measurement Based Quantum Computation

  • Damian Markham
  • Elham Kashefi
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Quantum Computation Logical Operator Cluster State Graph State Resource State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Damian Markham
    • 1
  • Elham Kashefi
    • 2
  1. 1.CNRS LTCI, Département Informatique et RéseauxTelecom ParisTechParis CEDEX 13France
  2. 2.School of InformaticsUniversity of EdinburghEdinburghUK

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