Optimal Parallel Quantum Query Algorithms

We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum algorithms as much as possible. We show tight bounds for a...

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Bibliographic Details
Published in:Algorithmica Vol. 79; no. 2; pp. 509 - 529
Main Authors: Jeffery, Stacey, Magniez, Frederic, de Wolf, Ronald
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2017
Springer Nature B.V
Springer Verlag
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Complexity
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Functions (mathematics)
Lower bounds
Mathematical analysis
Mathematics of Computing
Parallel processing
Qubits (quantum computing)
Queries
Theory of Computation
Upper bounds
Quantum algorithms
Lower bounds
Query complexity
Parallel algorithms
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum algorithms as much as possible. We show tight bounds for a number of problems, specifically Θ ( ( n / p ) 2 / 3 ) p -parallel queries for element distinctness and Θ ( ( n / p ) k / ( k + 1 ) ) for k -sum. Our upper bounds are obtained by parallelized quantum walk algorithms, and our lower bounds are based on a relatively small modification of the adversary lower bound method, combined with recent results of Belovs et al. on learning graphs. We also prove some general bounds, in particular that quantum and classical p -parallel query complexity are polynomially related for all total functions  f when p is small compared to f ’s block sensitivity.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-016-0206-z