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

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


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.


Quantum Algorithms Span Programs Quantum Query Linear Algebraic Model Witness Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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