The quantum query complexity of certification

Details The quantum query complexity of certification The quantum query complexity of certification

2009-03-06

arxiv.org/abs/0903.1291v1

Quantum Information and Computation 10, 181-188 (2010)

Physics

Quantum Physics

8 pages

Scientific paper

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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