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arXiv · 0903.1291

The quantum query complexity of certification

Andris Ambainis·Andrew M. Childs·François Le Gall·Seiichiro Tani
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Abstract

We study the quantum query complexity of finding a certificate for a d-regular, k-level balanced NAND formula. Up to logarithmic factors, we show that the query complexity is Theta(d^{(k+1)/2}) for 0-certificates, and Theta(d^{k/2}) for 1-certificates. In particular, this shows that the zero-error quantum query complexity of evaluating such formulas is O(d^{(k+1)/2}) (again neglecting a logarithmic factor). Our lower bound relies on the fact that the quantum adversary method obeys a direct sum theorem.

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Andris Ambainis, Andrew M. Childs, François Le Gall, Seiichiro Tani. 2009-03-06. The quantum query complexity of certification. https://doi.org/10.26421/qic10.3-4

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