5 research outputs found
Obtaining the Quantum Fourier Transform from the Classical FFT with QR Decomposition
We present the detailed process of converting the classical Fourier Transform
algorithm into the quantum one by using QR decomposition. This provides an
example of a technique for building quantum algorithms using classical ones.
The Quantum Fourier Transform is one of the most important quantum subroutines
known at present, used in most algorithms that have exponential speed up
compared to the classical ones. We briefly review Fast Fourier Transform and
then make explicit all the steps that led to the quantum formulation of the
algorithm, generalizing Coppersmith's work.Comment: 12 pages, 1 figure (generated within LaTeX). To appear in Journal of
Computational and Applied Mathematic
The QWalk Simulator of Quantum Walks
Several research groups are giving special attention to quantum walks
recently, because this research area have been used with success in the
development of new efficient quantum algorithms. A general simulator of quantum
walks is very important for the development of this area, since it allows the
researchers to focus on the mathematical and physical aspects of the research
instead of deviating the efforts to the implementation of specific numerical
simulations. In this paper we present QWalk, a quantum walk simulator for one-
and two-dimensional lattices. Finite two-dimensional lattices with generic
topologies can be used. Decoherence can be simulated by performing measurements
or by breaking links of the lattice. We use examples to explain the usage of
the software and to show some recent results of the literature that are easily
reproduced by the simulator.Comment: 21 pages, 11 figures. Accepted in Computer Physics Communications.
Simulator can be downloaded from http://qubit.lncc.br/qwal
Quantum walks: a comprehensive review
Quantum walks, the quantum mechanical counterpart of classical random walks,
is an advanced tool for building quantum algorithms that has been recently
shown to constitute a universal model of quantum computation. Quantum walks is
now a solid field of research of quantum computation full of exciting open
problems for physicists, computer scientists, mathematicians and engineers.
In this paper we review theoretical advances on the foundations of both
discrete- and continuous-time quantum walks, together with the role that
randomness plays in quantum walks, the connections between the mathematical
models of coined discrete quantum walks and continuous quantum walks, the
quantumness of quantum walks, a summary of papers published on discrete quantum
walks and entanglement as well as a succinct review of experimental proposals
and realizations of discrete-time quantum walks. Furthermore, we have reviewed
several algorithms based on both discrete- and continuous-time quantum walks as
well as a most important result: the computational universality of both
continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing
Journa