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The quantum algorithm of Kieu does not solve the Hilbert's tenth problem

Boris Tsirelson
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Abstract

Recently T. Kieu (arXiv:quant-ph/0110136) claimed a quantum algorithm computing some functions beyond the Church-Turing class. He notes that "it is in fact widely believed that quantum computation cannot offer anything new about computability" and claims the opposite. However, his quantum algorithm does not work, which is the point of my short note. I still believe that quantum computation leads to new complexity but retains the old computability.

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Boris Tsirelson. 2001-11-01. The quantum algorithm of Kieu does not solve the Hilbert's tenth problem. https://arxiv.org/abs/quant-ph/0111009

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