Resources Required for Preparing Graph States

Abstract : 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 graphs states. Using a novel graph-contraction procedure, we show that any graph state can be prepared by a linear-size constant-depth quantum circuits, 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.
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Peter Høyer, Mehdi Mhalla, Simon Perdrix. Resources Required for Preparing Graph States. 17th International Symposium on Algorithms and Computation (ISAAC 2006), Dec 2006, Kolkata, India. pp.638 - 649, ⟨10.1007/11940128_64⟩. ⟨hal-01378771⟩

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