Resources Required for Preparing Graph States

  • Peter Høyer
  • Mehdi Mhalla
  • Simon Perdrix
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


Graph states have become a key class of states within quantum computation. They form a basis for universal quantum computation, capture key properties of entanglement, are related to quantum error correction, establish links to graph theory, violate Bell inequalities, and have elegant and short graph-theoretical descriptions. We give here a rigorous analysis of the resources required for producing graph states. Using a novel graph-contraction procedure, we show that any graph state can be prepared by a linear-size constant-depth quantum circuit, and we establish trade-offs between depth and width. We show that any minimal-width quantum circuit requires gates that acts on several qubits, regardless of the depth. We relate the complexity of preparing graph states to a new graph-theoretical concept, the local minimum degree, and show that it captures basic properties of graph states.


Quantum Computing Algorithms Foundations of computing 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Peter Høyer
    • 1
  • Mehdi Mhalla
    • 2
  • Simon Perdrix
    • 2
  1. 1.Dept. of Comp. Sci.University of CalgaryCanada
  2. 2.Leibniz LaboratoryGrenobleFrance

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