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BQPp = PP for integer p > 2

2011/06/03 by Joseph Bebel, Henry Yuen, Bebel, Joseph +1
Computer Science · Physics and Astronomy · #Complexity and Algorithms in Graphs #Computability, Logic, AI Algorithms #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #cs.CC #quant-ph

paper · pdf · doi:10.48550/arxiv.1106.0572

This paper has been withdrawn by the authors due to the fact that strong error reduction for BQP_p problems is significantly more subtle than demonstrated, which compromises the main result

openalex publication_date 2011/06/03 · arxiv created 2011/06/22 · arxiv updated 2011/06/23 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

There's something really strange about quantum mechanics. It's not just that cats can be dead and alive at the same time, and that entanglement seems to violate the principle of locality; quantum mechanics seems to be what Aaronson calls "an island in theoryspace", because even slight perturbations to the theory of quantum mechanics seem to generate absurdities. In [Aar 04] and [Aar 05], he explores these perturbations and the corresponding absurdities in the context of computation. In particular, he shows that a quantum theory where the measurement probabilities are computed using p-norm instead of the standard 2-norm has the effect of blowing up the class BQP (the class of problems that can be efficiently solved on a quantum computer) to at least PP (the class of problems that can be solved in probabilistic polynomial time). He showed that PP ⊆ BQPp ⊆ PSPACE for all constants p != 2, and that BQPp = PP for even integers p > 2. Here, we show that this equality holds for all integers p > 2.

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