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Paper:

TR05-003 | 23rd December 2004 00:00

Quantum Computing, Postselection, and Probabilistic Polynomial-Time

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TR05-003
Authors: Scott Aaronson
Publication: 9th January 2005 21:51
Downloads: 1260
Keywords: 


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 Polynomial-Time. Using this result, I show that several simple changes to the axioms of quantum mechanics would let us solve PP-complete 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.



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