In this talk, we describe two recent developments in quantum algorithms.

The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time \(O(\sqrt{N})\). This provides quantum speedups for any problem that can be expressed via Boolean formulas. This result can be also extended to span problems, a generalization of Boolean formulas. This provides an optimal quantum algorithm for any Boolean function in the black-box query model.

The second new development is a quantum algorithm for solving systems of linear equations. In contrast with traditional algorithms that run in time O(N 2.37...) where N is the size of the system, the quantum algorithm runs in time O(log c N). It outputs a quantum state describing the solution of the system.


Boolean Function Quantum Algorithm Discrete Logarithm Quantum Walk Boolean Formula 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Andris Ambainis
    • 1
  1. 1.Faculty of ComputingUniversity of LatviaRigaLatvia

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