Quantum Computing, Postselection, and Probabilistic Polynomial-Time

Details Quantum Computing, Postselection, and Probabilistic Polynomial-Time Quantum Computing, Postselection, and Probabilistic Polynomial-Time

2004-12-23

arxiv.org/abs/quant-ph/0412187v1

Physics

Quantum Physics

8 pages, 1 figure. Supersedes the computational results in quant-ph/0401062

Scientific paper

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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