Quantum computing, postselection, and probabilistic polynomial-time
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.
- Publication:
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Proceedings of the Royal Society of London Series A
- Pub Date:
- November 2005
- DOI:
- Bibcode:
- 2005RSPSA.461.3473A
- Keywords:
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- quantum computers;
- computational complexity;
- Born's rule