Adversary Lower Bounds for Nonadaptive Quantum Algorithms
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
Quantum approaches to graph colouring
Theoretical Computer Science
Claw finding algorithms using quantum walk
Theoretical Computer Science
Adversary lower bounds for nonadaptive quantum algorithms
Journal of Computer and System Sciences
Can quantum search accelerate evolutionary algorithms?
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Quantum property testing for bounded-degree graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Realizing reversible circuits using a new class of quantum gates
Proceedings of the 49th Annual Design Automation Conference
Improving quantum query complexity of boolean matrix multiplication using graph collision
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
The quantum query complexity of read-many formulas
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
On the "Q" in QMDDs: efficient representation of quantum functionality in the QMDD data-structure
RC'13 Proceedings of the 5th international conference on Reversible Computation
Considering nearest neighbor constraints of quantum circuits at the reversible circuit level
Quantum Information Processing
Hi-index | 0.00 |
Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity, Strong Connectivity, Minimum Spanning Tree, and Single Source Shortest Paths. For example, we show that the query complexity of Minimum Spanning Tree is in $\Theta(n^{3/2})$ in the matrix model and in $\Theta(\sqrt{nm})$ in the array model, while the complexity of Connectivity is also in $\Theta(n^{3/2})$ in the matrix model but in $\Theta(n)$ in the array model. The upper bounds utilize search procedures for finding minima of functions under various conditions.