Quantum computing, postselection, and probabilistic polynomial-time

@article{Aaronson2005QuantumCP,
  title={Quantum computing, postselection, and probabilistic polynomial-time},
  author={Scott Aaronson},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  year={2005},
  volume={461},
  pages={3473 - 3482}
}
  • S. Aaronson
  • Published 23 December 2004
  • Computer Science, Mathematics, Physics
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
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… 
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