The quantum query complexity of certification
arXiv preprint arXiv:0903.1291, 2009•arxiv.org
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.
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.
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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