Applications of the Adversary Method in Quantum Query Algorithms
Abstract
In the thesis, we use a recently developed tight characterisation of quantum query complexity, the adversary bound, to develop new quantum algorithms and lower bounds. Our results are as follows: * We develop a new technique for the construction of quantum algorithms: learning graphs. * We use learning graphs to improve quantum query complexity of the triangle detection and the $k$distinctness problems. * We prove tight lower bounds for the $k$sum and the triangle sum problems. * We construct quantum algorithms for some subgraphfinding problems that are optimal in terms of query, time and space complexities. * We develop a generalisation of quantum walks that connects electrical properties of a graph and its quantum hitting time. We use it to construct a timeefficient quantum algorithm for 3distinctness.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.3858
 Bibcode:
 2014arXiv1402.3858B
 Keywords:

 Quantum Physics
 EPrint:
 PhD Thesis, 169 pages