Quantum complexity theory: Difference between revisions

Revision as of 07:40, 3 March 2020

Revision as of 07:41, 3 March 2020

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==Overview==

A complexity class is a collection of problems whichthat can be solved by some computational model under resource constraints. For instance, the complexity class [[P (complexity)|P]] is defined to be the set of problems solvable by a [[Turing machine]] in [[polynomial time]]. Similarly, one may define a quantum complexity class using a quantum model of computation, such as a standard [[quantum computer]] or a [[quantum Turing machine]]. Thus, the complexity class [[BQP]] is defined to be the set of problems solvable by a quantum computer in polynomial time with bounded error.

Two important quantum complexity classes are [[BQP]] and [[QMA]] which are the bounded-error quantum analogues of [[P (complexity)|P]] and [[NP (complexity)|NP]]. One of the main aims of quantum complexity theory is to find out where these classes lie with respect to classical complexity classes such as P, NP, [[PP (complexity)|PP]], [[PSPACE]] and [[List of complexity classes|other complexity classes]].