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Time- and Query-optimal Quantum Algorithms Based on Decision Trees

May 18, 2021

44 pages

Published in:

ACM Trans.Quant.Comput. 3 (2022) 4, 19

Published: Jul 27, 2022

e-Print:

2105.08309 [quant-ph]

DOI:

10.1145/3519269

View in:

ADS Abstract Service

reference search4 citations

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Abstract: (Association for Computing Machinery)

It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity O(√ GT where T is the query complexity of the classical algorithm (depth of the decision tree) and G is the maximum number of wrong answers by the guessing algorithm [3, 14]. In this article, we show that, given some constraints on the classical algorithms, this quantum algorithm can be implemented in time Õ(√ GT). Our algorithm is based on non-binary span programs and their efficient implementation. We conclude that various graph-theoretic problems including bipartiteness, cycle detection, and topological sort can be solved in time O(n

^{3/2}

log

^{2}

n) and with O(n

^{3/2}

) quantum queries. Moreover, finding a maximal matching can be solved with O(n

^{3/2}

) quantum queries in time O(n

^{3/2}

log

^{2}

n), and maximum bipartite matching can be solved in time O(n

^{2}

log

^{2}

n).

Note:

44 pages

Quantum query complexity
quantum algorithms
span programs
quantum time complexity
quantum algorithm
topological

References(18)

Figures(7)

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