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Quantum
Information and Computation
ISSN: 1533-7146
published since 2001
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Vol.14 No.9&10 July 2014 |
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Polynomial time quantum algorithms for certain bivariate hidden
polynomial problems
(pp0790-0806)
Thomas
Decker, Peter Hoyer, Gabor Ivanyos, and Miklos Santha
doi:
https://doi.org/10.26421/QIC14.9-10-6
Abstracts:
We present a new method for solving the hidden polynomial
graph problem (HPGP) which is a special case of the hidden polynomial
problem (HPP). The new approach yields an efficient quantum algorithm
for the bivariate HPGP even when the input consists of several level set
superpositions, a more difficult version of the problem than the one
where the input is given by an oracle. For constant degree, the
algorithm is polylogarithmic in the size of the base field. We also
apply the results to give an efficient quantum algorithm for the oracle
version of the HPP for an interesting family of bivariate hidden
functions. This family includes diagonal quadratic forms and elliptic
curves.
Key words:
Quantum algorithm, Hidden Polynomial Problem |
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