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arXiv quant-ph/0412187quant-phcs.CC
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量子计算、后选择和概率多项式时间

Quantum Computing, Postselection, and Probabilistic Polynomial-Time

Scott Aaronson

摘要:

我研究了量子计算机可以有效解决的一类问题,因为它能够对测量结果进行“后选择”。我证明了这个类与一个经典的复杂性类称为PP,或概率多项式时间。使用这个结果,我表明,几个简单的变化,量子力学的公理将让我们有效地解决PP-完全问题。这个结果也暗示着,作为一个简单的推论,Beigel,Reingold和Spielman的一个著名定理,即PP在交集下是封闭的,以及Fortnow和Reingold的定理的推广。这说明,量子计算可以产生新的和更简单的证明有关经典计算的主要结果。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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