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Optimal quantum query bounds for almost all Boolean functions

Authors Andris Ambainis, Arturs Backurs, Juris Smotrovs, Ronald de Wolf

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LIPIcs.STACS.2013.446.pdf
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  • Quantum computing
  • query complexity
  • lower bounds
  • polynomial method

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Abstract

We show that almost all n-bit Boolean functions have bounded-error quantum query complexity at least n/2, up to lower-order terms. This improves over an earlier n/4 lower bound of Ambainis (A. Ambainis, 1999), and shows that van Dam's oracle interrogation (W. van Dam, 1998) is essentially optimal for almost all functions. Our proof uses the fact that the acceptance probability of a T-query algorithm can be written as the sum of squares of degree-T polynomials.

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Andris Ambainis, Arturs Backurs, Juris Smotrovs, and Ronald de Wolf. Optimal quantum query bounds for almost all Boolean functions. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 446-453, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013) https://doi.org/10.4230/LIPIcs.STACS.2013.446

Author Details

Andris Ambainis
Arturs Backurs
Juris Smotrovs
Ronald de Wolf
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