Quantum computing, postselection, and probabilistic (2005)
| Venue: | Proceedings of the Royal Society A |
| Citations: | 32 - 8 self |
BibTeX
@INPROCEEDINGS{Aaronson05quantumcomputing,,
author = {Scott Aaronson},
title = {Quantum computing, postselection, and probabilistic},
booktitle = {Proceedings of the Royal Society A},
year = {2005},
pages = {0412187}
}
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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.
