Quantum Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees

We present two algorithms in the Quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability; one for producing an approximately optimal Steiner Tree, and one for producing an exact directed minimum spanning tree, each of which uses \overline{O}(n^{1/4}) rounds of comm...

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Bibliographic Details
Published in2023 IEEE International Conference on Quantum Computing and Engineering (QCE) Vol. 1; pp. 1249 - 1259
Main Authors Kerger, Phillip A., Bernal Neira, David E., Izquierdo, Zoe Gonzalez, Rieffel, Eleanor G.
Format Conference Proceeding
LanguageEnglish
Published IEEE 17.09.2023
Subjects
Approximation algorithms
Complexity theory
Computational modeling
Directed Minimum Spanning Tree
Distributed algorithms
Distributed Computing
Quantum computing
Steiner Tree
Steiner trees
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Summary:We present two algorithms in the Quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability; one for producing an approximately optimal Steiner Tree, and one for producing an exact directed minimum spanning tree, each of which uses \overline{O}(n^{1/4}) rounds of communication and \tilde{O}(n^{9/4}) messages, achieving a lower asymptotic round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. At a high level, we achieve these results by combining classical algorithmic frameworks with quantum subroutines. Additionally, we characterize the constants and logarithmic factors involved in our algorithms as well as related classical algorithms, otherwise obscured by \overline{O} notation, revealing that advances are needed to render both the quantum and classical algorithms practical.
DOI:10.1109/QCE57702.2023.00141