POLYNOMIAL TIME QUANTUM ALGORITHMS FOR CERTAIN BIVARIATE HIDDEN POLYNOMIAL PROBLEMS

被引：0

作者：

Decker, Thomas ^{[1
]}

Hoyer, Peter ^{[2
,3
]}

Ivanyos, Gabor ^{[4
]}

Santha, Miklos ^{[1
,5
]}

机构：

[1] Natl Univ Singapore, Ctr Quantum Technol, Singapore 117543, Singapore

[2] Univ Calgary, Dept Comp Sci, Calgary, AB T2N 1N4, Canada

[3] Univ Calgary, Inst Quantum Sci & Technol, Calgary, AB T2N 1N4, Canada

[4] Hungarian Acad Sci, Inst Comp Sci & Control, H-1111 Budapest, Hungary

[5] Univ Paris Diderot, CNRS, LIAFA, F-75013 Paris, France

来源：

QUANTUM INFORMATION & COMPUTATION | 2014年 / 14卷 / 9-10期

基金：

新加坡国家研究基金会; 匈牙利科学研究基金会; 加拿大自然科学与工程研究理事会;

关键词：

Quantum algorithm; Hidden Polynomial Problem; SUBGROUP PROBLEM;

D O I：

暂无

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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.

引用

页码：790 / 806

页数：17

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