18,480 research outputs found
A study of the communication cost of the FFT on torus multicomputers
The computation of a one-dimensional FFT on a c-dimensional torus multicomputer is analyzed. Different approaches are proposed which differ in the way they use the interconnection network. The first approach is based on the multidimensional index mapping technique for the FFT computation. The second approach starts from a hypercube algorithm and then embeds the hypercube onto the torus. The third approach reduces the communication cost of the hypercube algorithm by pipelining the communication operations. A novel methodology to pipeline the communication operations on a torus is proposed. Analytical models are presented to compare the different approaches. This comparison study shows that the best approach depends on the number of dimensions of the torus and the communication start-up and transfer times. The analytical models allow us to select the most efficient approach for the available machine.Peer ReviewedPostprint (published version
General-Purpose Parallel Simulator for Quantum Computing
With current technologies, it seems to be very difficult to implement quantum
computers with many qubits. It is therefore of importance to simulate quantum
algorithms and circuits on the existing computers. However, for a large-size
problem, the simulation often requires more computational power than is
available from sequential processing. Therefore, the simulation methods using
parallel processing are required.
We have developed a general-purpose simulator for quantum computing on the
parallel computer (Sun, Enterprise4500). It can deal with up-to 30 qubits. We
have performed Shor's factorization and Grover's database search by using the
simulator, and we analyzed robustness of the corresponding quantum circuits in
the presence of decoherence and operational errors. The corresponding results,
statistics and analyses are presented.Comment: 15 pages, 15 figure
On Polynomial Multiplication in Chebyshev Basis
In a recent paper Lima, Panario and Wang have provided a new method to
multiply polynomials in Chebyshev basis which aims at reducing the total number
of multiplication when polynomials have small degree. Their idea is to use
Karatsuba's multiplication scheme to improve upon the naive method but without
being able to get rid of its quadratic complexity. In this paper, we extend
their result by providing a reduction scheme which allows to multiply
polynomial in Chebyshev basis by using algorithms from the monomial basis case
and therefore get the same asymptotic complexity estimate. Our reduction allows
to use any of these algorithms without converting polynomials input to monomial
basis which therefore provide a more direct reduction scheme then the one using
conversions. We also demonstrate that our reduction is efficient in practice,
and even outperform the performance of the best known algorithm for Chebyshev
basis when polynomials have large degree. Finally, we demonstrate a linear time
equivalence between the polynomial multiplication problem under monomial basis
and under Chebyshev basis
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