Quantum interpolation of polynomilas

Authors:
Daniel M. Kane;Samuel A. Kutin
Affiliations:
Dept. of Mathematics, Harvard University, Cambridge MA;IDA/CCR-P, Bunn Drive, Princeton NJ
Venue:
Quantum Information & Computation
Year:
2011

Citing 13
Cited 1

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Span Programs and Quantum Query Complexity: The General Adversary Bound Is Nearly Tight for Every Boolean Function

FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science

On the uselessness of quantum queries

Theoretical Computer Science

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Abstract

Can a quantum computer efficiently interpolate polynomials? We consider black-boxalgorithms that seek to learn information about a polynomial f from input/output pairs(xi, f(xi)). We define a more general class of (d, S)-independent function properties,where, outside of a set S of exceptions, knowing d input values does not help one predictthe answer. There are essentially two strategies to computing such a function: queryd + 1 random input values, or search for one of the |S| exceptions. We show that, up toconstant factors, we cannot beat these two approaches.