Quantum computation in algebraic number theory: Hallgren’s efficient quantum algorithm for solving Pell’s equation

Pell’s equation is x 2− dy 2=1, where d is a square-free integer and we seek positive integer solutions x, y>0. Let ( x 0, y 0) be the smallest solution (i.e., having smallest A=x 0+y 0 d ). Lagrange showed that every solution can easily be constructed from A so given d it suffices to compute A....

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Bibliographic Details

Published in:	Annals of physics Vol. 306; no. 2; pp. 241 - 279
Main Author:	Jozsa, Richard
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.08.2003
Subjects:	Pell’s equation Quantum algorithms Quantum Fourier transform Quantum Fourier transform Quantum algorithms Pell’s equation
ISSN:	0003-4916, 1096-035X
Online Access:	Get full text
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