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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 ..."
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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
Extending scientific computing system with structural quantum programming capabilities
, 2010
"... Abstract. We present the basic highlevel structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudocode based on QCL quantum programming language to describe them. We also present ..."
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Abstract. We present the basic highlevel structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudocode based on QCL quantum programming language to describe them. We also present the implementation of introduced structures in GNU Octave language for scientific computing. Procedures used in the implementation are available as a package quantumoctave providing library of functions, which facilitates the simulation of quantum computing. This package allows also to incorporate highlevel programming concepts into the simulation in GNU Octave and Matlab. As such it connects features unique for higllevel quantum programming languages, with the full palette of efficient computational routines commonly available in modern scientific computing systems. To present the major features of the described package we provide the implementation of selected quantum algorithms. We also show how quantum errors can be taken into account during the simulation of quantum algorithms using quantumoctave package. This is possible thanks to the ability to operate on density matrices implemented in quantumoctave. Key words: quantum information, quantum programming, models of quantum computation. 1.