Quantum Search on Computation Trees
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TL;DR
This paper generalizes quantum walk algorithms for search in backtracking trees with variable vertex computation times, leading to optimal query complexity algorithms for variable time search and improved geometric intersection detection.
Contribution
It introduces a simple, explicit quantum algorithm framework that handles variable vertex computation times, resolving open questions and improving existing algorithms.
Findings
Achieves $ ext{O}( ext{sqrt}(TD))$ query complexity for detection in variable-time trees.
Provides an optimal $ ext{O}( ext{sqrt}(T ext{log} ext{min}(n,t_{max})))$ algorithm for variable time search.
Improves geometric intersection detection to $ ilde{O}(n)$ time.
Abstract
We show a simple generalization of the quantum walk algorithm for search in backtracking trees by Montanaro (ToC 2018) to the case where vertices can have different times of computation. If a vertex in the tree of depth is computed in steps from its parent, then we show that detection of a marked vertex requires queries to the steps of the computing procedures, where . This framework provides an easy and convenient way to re-obtain a number of other quantum frameworks like variable time search, quantum divide & conquer and bomb query algorithms. The underlying algorithm is simple, explicitly constructed, and has low poly-logarithmic factors in the complexity. As a corollary, this gives a quantum algorithm for variable time search with unknown times with optimal query complexity , where $T =…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Complexity and Algorithms in Graphs · Advanced Graph Theory Research
