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Quantum Optimization

The quantum query complexity of learning multilinear polynomials

arXiv

Authors: Ashley Montanaro

Year

2011

Paper ID

8797

Status

Preprint

Abstract Read

~2 min

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Abstract

In this note we study the number of quantum queries required to identify an unknown multilinear polynomial of degree d in n variables over a finite field F_q. Any bounded-error classical algorithm for this task requires Omegan^d queries to the polynomial. We give an exact quantum algorithm that uses On^(d-1) queries for constant d, which is optimal. In the case q=2, this gives a quantum algorithm that uses On^(d-1) queries to identify a codeword picked from the binary Reed-Muller code of order d.

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In this note we study the number of quantum queries required to identify an unknown multilinear polynomial of degree d in n variables over a finite field F_q.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1105.3310 [2] arXiv https://arxiv.org/abs/1105.3310 [3] Publisher https://arxiv.org/abs/1105.3310

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