Quantum computing, postselection, and probabilistic polynomialtime
Abstract
I study the class of problems efficiently solvable by a quantum computer, given the ability to ‘postselect’ on the outcomes of measurements. I prove that this class coincides with a classical complexity class called PP, or probabilistic polynomialtime. Using this result, I show that several simple changes to the axioms of quantum mechanics would let us solve PPcomplete problems efficiently. The result also implies, as an easy corollary, a celebrated theorem of Beigel, Reingold and Spielman that PP is closed under intersection, as well as a generalization of that theorem due to Fortnow and Reingold. This illustrates that quantum computing can yield new and simpler proofs of major results about classical computation.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 November 2005
 DOI:
 10.1098/rspa.2005.1546
 Bibcode:
 2005RSPSA.461.3473A
 Keywords:

 quantum computers;
 computational complexity;
 Born's rule