Digraph decompositions and Eulerian systems
SIAM Journal on Algebraic and Discrete Methods
Connectivity of isotropic systems
Proceedings of the third international conference on Combinatorial mathematics
Journal of Combinatorial Theory Series B
Approximating rank-width and clique-width quickly
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Simple sets of measurements for universal quantum computation and graph state preparation
TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
On the minimum degree up to local complementation: bounds and complexity
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Pseudo-telepathy games and genuine ns k-way nonlocality using graph states
Quantum Information & Computation
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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.