Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Quantum Algorithms and Complexity for Continuous Problems

  • Anargyros Papageorgiou
  • Joseph F. Traub
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_424-3

Definition of the Subject

Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we are dealing with a numerical approximation to the solution.

There are two major motivations for studying quantum algorithms and complexity for continuous problems:
  1. 1.

    Are quantum computers more powerful than classical computers for important scientific problems? How much more powerful? This would answer the question posed by Nielsen and Chuang (2000, p. 47).

  2. 2.

    Many important scientific and engineering problems have continuous formulations. These problems occur in fields such as physics, chemistry, engineering, and finance. The continuous formulations include path integration, partial differential equations (in particular, the Schrödinger equation), and continuous optimization.


To answer the first question, we must know the classical computational complexity (for brevity, complexity) of the...


Boolean Function Quantum Computer Path Integration Quantum Algorithm Query Complexity 
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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We are grateful to Erich Novak, University of Jena, and Henryk Woźniakowski, Columbia University and University of Warsaw, for their very helpful comments. We thank Jason Petras, Columbia University, for checking the complexity estimates appearing in the tables.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Computer Science DepartmentColumbia UniversityNew YorkUSA