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Span-Program-Based Quantum Algorithms for Graph Bipartiteness and Connectivity

  • Agnis ĀriņšEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9548)

Abstract

Span program is a linear-algebraic model of computation which can be used to design quantum algorithms. For any Boolean function there exists a span program that leads to a quantum algorithm with optimal quantum query complexity. In general, finding such span programs is not an easy task.

In this work, given a query access to the adjacency matrix of a simple graph G with n vertices, we provide two new span-program-based quantum algorithms:
  • an algorithm for testing if the graph is bipartite that uses \(O(n\sqrt{n})\) quantum queries;

  • an algorithm for testing if the graph is connected that uses \(O(n\sqrt{n})\) quantum queries.

Notes

Acknowledgements

I am grateful to Andris Ambainis for the suggestion to solve the graph problems with span programs, and for many useful comments during the development of the paper.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of LatviaRigaLatvia

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