2005/09/05 by Scott Aaronson · 16 citations
Computer Science · #Complexity and Algorithms in Graphs #Computability, Logic, AI Algorithms #Quantum Computing Algorithms and Architecture
paper · doi:10.1098/rspa.2005.1546
openalex publication_date 2005/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/26
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.