Quantum computing, postselection, and probabilistic polynomial-time

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.

# Quantum Computing Algorithms and Architecture # Computer Science # Complexity and Algorithms in Graphs # Quantum Information and Cryptography

Scott Aaronson (2005). "Quantum computing, postselection, and probabilistic polynomial-time". Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences. https://doi.org/10.1098/rspa.2005.1546