Results 1 
4 of
4
Quantum hidden subgroup algorithms on free groups, (in preparation
"... Abstract. One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the DeutschJozsa, Simon, Shor algorithms, and many more. In thi ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
(Show Context)
Abstract. One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the DeutschJozsa, Simon, Shor algorithms, and many more. In this paper, our strategy for finding new quantum algorithms is to decompose Shor’s quantum factoring algorithm into its basic primitives, then to generalize these primitives, and finally to show how to reassemble them into new QHS algorithms. Taking an ”alphabetic building blocks approach, ” we use these primitives to form an ”algorithmic toolkit ” for the creation of new quantum algorithms, such as wandering Shor algorithms, continuous Shor algorithms, the quantum circle algorithm, the dual Shor algorithm, a QHS algorithm for Feynman integrals, free QHS algorithms, and more. Toward the end of this paper, we show how Grover’s algorithm is most surprisingly “almost ” a QHS algorithm, and how this result suggests the possibility of an even more complete ”algorithmic tookit ” beyond the QHS algorithms. Contents
Quantum Algorithms in group theory
, 2003
"... We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
DELTA FUNCTION FOR AN AFFINE SUBSPACE
"... Abstract. The Kubo{Yokoi and Donsker delta functions are well known generalized functions in innite dimensional distribution theory. In this paper we develop the delta function for an ane subspace and show that it is a generalization of the Kubo{Yokoi and Donsker delta functions. The Wiener{Itô e ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. The Kubo{Yokoi and Donsker delta functions are well known generalized functions in innite dimensional distribution theory. In this paper we develop the delta function for an ane subspace and show that it is a generalization of the Kubo{Yokoi and Donsker delta functions. The Wiener{Itô expansion of the delta function for an ane subspace is also given.
1 White Noise Analysis: Background and a Recent Application
, 2007
"... We present a description of the framework of white noise analysis as an innitedimensional distribution theory. We then describe some recent developments in the context of an application arising from quantum computing. 1. ..."
Abstract
 Add to MetaCart
(Show Context)
We present a description of the framework of white noise analysis as an innitedimensional distribution theory. We then describe some recent developments in the context of an application arising from quantum computing. 1.