Hallgren, Sean - Department of Computer Science and Engineering, Pennsylvania State University

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Hallgren, Sean - Department of Computer Science and Engineering, Pennsylvania State University

Fast Quantum Algorithms for Computing the Unit Group and Class Group of a Number Field
Quantum Fourier Sampling, the Hidden Subgroup Problem, and Beyond Sean Joseph Hallgren
Limitations of quantum coset states for graph isomorphism Sean Hallgren
Introduction In 1994, Peter Shor [45] made a huge discovery in the eld of quantum computing.
Fourier Sampling and the HSP In this chapter we will discuss the problems that can be eciently solved by
Fast Quantum Algorithms for Computing the Unit Group and Class Group of a Number Field
Fourier Sampling over Abelian 5.1 Introduction
Fourier Sampling Coset States of Nonabelian Groups
We have given a new quantum Fourier sampling theorem and a new quantum Fourier transform algorithm for abelian groups. These results are based on the robustness
Quantum Fourier Sampling, the Hidden Subgroup Problem, and Beyond Sean Joseph Hallgren
Preliminaries Let C denote the eld of complex numbers. For 2 C let or denote the
Ecient Quantum Algorithms for Shifted Quadratic Character
In this chapter we will describe the model of a quantum computer, what a quan-tum algorithm is, and what makes such an algorithm ecient. We will rst give a short
Bibliography [1] Mikl os Ajtai and Cynthia Dwork. A public-key cryptosystem with worst-case/average-
PolynomialTime Quantum Algorithms for Pell's Equation and the Principal Ideal Problem #
SIAM J. COMPUT. c XXXX Society for Industrial and Applied Mathematics Vol. 0, No. 0, pp. 000000
Polynomial-Time Quantum Algorithms for Pell's Equation and the Principal Ideal Problem