15,433 research outputs found
Optimal Control Theory for Continuous Variable Quantum Gates
We apply the methodology of optimal control theory to the problem of
implementing quantum gates in continuous variable systems with quadratic
Hamiltonians. We demonstrate that it is possible to define a fidelity measure
for continuous variable (CV) gate optimization that is devoid of traps, such
that the search for optimal control fields using local algorithms will not be
hindered. The optimal control of several quantum computing gates, as well as
that of algorithms composed of these primitives, is investigated using several
typical physical models and compared for discrete and continuous quantum
systems. Numerical simulations indicate that the optimization of generic CV
quantum gates is inherently more expensive than that of generic discrete
variable quantum gates, and that the exact-time controllability of CV systems
plays an important role in determining the maximum achievable gate fidelity.
The resulting optimal control fields typically display more complicated Fourier
spectra that suggest a richer variety of possible control mechanisms. Moreover,
the ability to control interactions between qunits is important for delimiting
the total control fluence. The comparative ability of current experimental
protocols to implement such time-dependent controls may help determine which
physical incarnations of CV quantum information processing will be the easiest
to implement with optimal fidelity.Comment: 39 pages, 11 figure
Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-like Transforms
We propose a novel method for constructing Hilbert transform (HT) pairs of
wavelet bases based on a fundamental approximation-theoretic characterization
of scaling functions--the B-spline factorization theorem. In particular,
starting from well-localized scaling functions, we construct HT pairs of
biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet
filters via a discrete form of the continuous HT filter. As a concrete
application of this methodology, we identify HT pairs of spline wavelets of a
specific flavor, which are then combined to realize a family of complex
wavelets that resemble the optimally-localized Gabor function for sufficiently
large orders.
Analytic wavelets, derived from the complexification of HT wavelet pairs,
exhibit a one-sided spectrum. Based on the tensor-product of such analytic
wavelets, and, in effect, by appropriately combining four separable
biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for
constructing 2D directional-selective complex wavelets. In particular,
analogous to the HT correspondence between the components of the 1D
counterpart, we relate the real and imaginary components of these complex
wavelets using a multi-dimensional extension of the HT--the directional HT.
Next, we construct a family of complex spline wavelets that resemble the
directional Gabor functions proposed by Daugman. Finally, we present an
efficient FFT-based filterbank algorithm for implementing the associated
complex wavelet transform.Comment: 36 pages, 8 figure
A pseudospectral matrix method for time-dependent tensor fields on a spherical shell
We construct a pseudospectral method for the solution of time-dependent,
non-linear partial differential equations on a three-dimensional spherical
shell. The problem we address is the treatment of tensor fields on the sphere.
As a test case we consider the evolution of a single black hole in numerical
general relativity. A natural strategy would be the expansion in tensor
spherical harmonics in spherical coordinates. Instead, we consider the simpler
and potentially more efficient possibility of a double Fourier expansion on the
sphere for tensors in Cartesian coordinates. As usual for the double Fourier
method, we employ a filter to address time-step limitations and certain
stability issues. We find that a tensor filter based on spin-weighted spherical
harmonics is successful, while two simplified, non-spin-weighted filters do not
lead to stable evolutions. The derivatives and the filter are implemented by
matrix multiplication for efficiency. A key technical point is the construction
of a matrix multiplication method for the spin-weighted spherical harmonic
filter. As example for the efficient parallelization of the double Fourier,
spin-weighted filter method we discuss an implementation on a GPU, which
achieves a speed-up of up to a factor of 20 compared to a single core CPU
implementation.Comment: 33 pages, 9 figure
A general framework for efficient FPGA implementation of matrix product
Original article can be found at: http://www.medjcn.com/ Copyright Softmotor LimitedHigh performance systems are required by the developers for fast processing of computationally intensive applications. Reconfigurable hardware devices in the form of Filed-Programmable Gate Arrays (FPGAs) have been proposed as viable system building blocks in the construction of high performance systems at an economical price. Given the importance and the use of matrix algorithms in scientific computing applications, they seem ideal candidates to harness and exploit the advantages offered by FPGAs. In this paper, a system for matrix algorithm cores generation is described. The system provides a catalog of efficient user-customizable cores, designed for FPGA implementation, ranging in three different matrix algorithm categories: (i) matrix operations, (ii) matrix transforms and (iii) matrix decomposition. The generated core can be either a general purpose or a specific application core. The methodology used in the design and implementation of two specific image processing application cores is presented. The first core is a fully pipelined matrix multiplier for colour space conversion based on distributed arithmetic principles while the second one is a parallel floating-point matrix multiplier designed for 3D affine transformations.Peer reviewe
Synthesis and Optimization of Reversible Circuits - A Survey
Reversible logic circuits have been historically motivated by theoretical
research in low-power electronics as well as practical improvement of
bit-manipulation transforms in cryptography and computer graphics. Recently,
reversible circuits have attracted interest as components of quantum
algorithms, as well as in photonic and nano-computing technologies where some
switching devices offer no signal gain. Research in generating reversible logic
distinguishes between circuit synthesis, post-synthesis optimization, and
technology mapping. In this survey, we review algorithmic paradigms ---
search-based, cycle-based, transformation-based, and BDD-based --- as well as
specific algorithms for reversible synthesis, both exact and heuristic. We
conclude the survey by outlining key open challenges in synthesis of reversible
and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table
Implementation of a Combined OFDM-Demodulation and WCDMA-Equalization Module
For a dual-mode baseband receiver for the OFDMWireless LAN andWCDMA standards, integration of the demodulation and equalization tasks on a dedicated hardware module has been investigated. For OFDM demodulation, an FFT algorithm based on cascaded twiddle factor decomposition has been selected. This type of algorithm combines high spatial and temporal regularity in the FFT data-flow graphs with a minimal number of computations. A frequency-domain algorithm based on a circulant channel approximation has been selected for WCDMA equalization. It has good performance, low hardware complexity and a low number of computations. Its main advantage is the reuse of the FFT kernel, which contributes to the integration of both tasks. The demodulation and equalization module has been described at the register transfer level with the in-house developed Arx language. The core of the module is a pipelined radix-23 butterfly combined with a complex multiplier and complex divider. The module has an area of 0.447 mm2 in 0.18 Âżm technology and a power consumption of 10.6 mW. The proposed module compares favorably with solutions reported in literature
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