Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Quantum Computational Complexity

  • John Watrous
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_428-3

Definition of the Subject

The inherent difficulty, or hardness, of computational problems is a fundamental concept in computational complexity theory. Hardness is typically formalized in terms of the resources required by different models of computation to solve problems, such as the number of steps of a deterministic Turing machine. A variety of models and resources are often considered, including deterministic, nondeterministic, and probabilistic models; time and space constraints; and interactions among models of differing abilities. Many interesting relationships among these different models and resource constraints are known.

One common feature of the most commonly studied computational models and resource constraints is that they are physically motivated. This is quite natural, given that computers are physical devices, and to a significant extent, it is their study that motivates and directs research on computational complexity. The predominant example is the class of...

Keywords

Turing Machine Quantum Circuit Quantum Operation Interactive Proof Toffoli Gate 
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 Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute for Quantum Computing and School of Computer ScienceUniversity of WaterlooWaterlooCanada