Quantum Noisy Rational Function Reconstruction

Hallgren, Sean; Russell, Alexander; Shparlinski, Igor E.

doi:10.1007/11533719_43

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…For instance, it can be approached by a quantum algorithm in the same style as in [10], where f is recovered from most significant bits of f (t) for some randomly chosen t ∈ F p . Moreover, classical algorithms of [3,4,8,11,15] can be adjusted to solve this problem.…”

Section: Theorem 14mentioning

confidence: 99%

Quantum period reconstruction of approximate sequences

Shparlinski

Winterhof

2007

Information Processing Letters

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Section: Theorem 14mentioning

confidence: 99%

Quantum period reconstruction of approximate sequences

Shparlinski

Winterhof

2007

Information Processing Letters

Self Cite

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“…Another idea to generalize abelian HSP is to consider Hidden Shift Problems [4,7] or problems with hidden non-linear structures [5,13,22]. In the latter context, we define and analyze a black-box problem that is based on polynomial functions of degree n ≥ 2 and that can be reduced to an instance of the yet unsolved Hidden Polynomial Problem (HPP) [5].…”

Section: Introductionmentioning

confidence: 99%

Efficient Quantum Algorithm for Identifying Hidden Polynomials

Decker,

Draisma,

Wocjan

2007

Preprint

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We consider a natural generalization of an abelian Hidden Subgroup Problem where the subgroups and their cosets correspond to graphs of linear functions over a finite field F with d elements. The hidden functions of the generalized problem are not restricted to be linear but can also be m-variate polynomial functions of total degree n ≥ 2.The problem of identifying hidden m-variate polynomials of degree less or equal to n for fixed n and m is hard on a classical computer since Ω( √ d) black-box queries are required to guarantee a constant success probability. In contrast, we present a quantum algorithm that correctly identifies such hidden polynomials for all but a finite number of values of d with constant probability and that has a running time that is only polylogarithmic in d.

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Efficient quantum algorithm for identifying hidden polynomials

Decker

Draisma

Wocjan

2009

QIC

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We consider a natural generalization of an abelian Hidden Subgroup Problem where the subgroups and their cosets correspond to graphs of linear functions over a finite field $\F$ with $d$ elements. The hidden functions of the generalized problem are not restricted to be linear but can also be $m$-variate polynomial functions of total degree $n\geq 2$. The problem of identifying hidden $m$-variate polynomials of degree less or equal to $n$ for fixed $n$ and $m$ is hard on a classical computer since $\Omega(\sqrt{d})$ black-box queries are required to guarantee a constant success probability. In contrast, we present a quantum algorithm that correctly identifies such hidden polynomials for all but a finite number of values of $d$ with constant probability and that has a running time that is only polylogarithmic in $d$.

show abstract

Quantum Noisy Rational Function Reconstruction

Cited by 3 publications

References 13 publications

Quantum period reconstruction of approximate sequences

Quantum period reconstruction of approximate sequences

Efficient Quantum Algorithm for Identifying Hidden Polynomials

Efficient quantum algorithm for identifying hidden polynomials

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