386 research outputs found
Transform processing and coding of images Final report
Transform processing and image codin
A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering
Since its emergence, quantum computing has enabled a wide spectrum of new possibilities and advantages, including its efficiency in accelerating computational processes exponentially. This has directed much research towards completely novel ways of solving a wide variety of engineering problems, especially through describing quantum versions of many mathematical tools such as Fourier and Laplace transforms, differential equations, systems of linear equations, and optimization techniques, among others. Exploration and development in this direction will revolutionize the world of engineering. In this manuscript, we review the state of the art of these emerging techniques from the perspective of quantum computer development and performance optimization, with a focus on the most common mathematical tools that support engineering applications. This review focuses on the application of these mathematical tools to quantum computer development and performance improvement/optimization. It also identifies the challenges and limitations related to the exploitation of quantum computing and outlines the main opportunities for future contributions. This review aims at offering a valuable reference for researchers in fields of engineering that are likely to turn to quantum computing for solutions. Doi: 10.28991/ESJ-2023-07-01-020 Full Text: PD
Basic concepts in quantum computation
Section headings: 1 Qubits, gates and networks 2 Quantum arithmetic and
function evaluations 3 Algorithms and their complexity 4 From interferometers
to computers 5 The first quantum algorithms 6 Quantum search 7 Optimal phase
estimation 8 Periodicity and quantum factoring 9 Cryptography 10 Conditional
quantum dynamics 11 Decoherence and recoherence 12 Concluding remarksComment: 37 pages, lectures given at les Houches Summer School on "Coherent
Matter Waves", July-August 199
Picture coding in viewdata systems
Viewdata systems in commercial use at present offer the facility
for transmitting alphanumeric text and graphic displays via the public
switched telephone network. An enhancement to the system would be to
transmit true video images instead of graphics. Such a system, under
development in Britain at present uses Differential Pulse Code Modulation
(DPCM) and a transmission rate of 1200 bits/sec. Error protection
is achieved by the use of error protection codes, which increases
the channel requirement.
In this thesis, error detection and correction of DPCM coded
video signals without the use of channel error protection is studied.
The scheme operates entirely at the receiver by examining the local
statistics of the received data to determine the presence of errors.
Error correction is then undertaken by interpolation from adjacent
correct or previousiy corrected data.
DPCM coding of pictures has the inherent disadvantage of a slow
build-up of the displayed picture at the receiver and difficulties with
image size manipulation. In order to fit the pictorial information
into a viewdata page, its size has to be reduced. Unitary transforms,
typically the discrete Fourier transform (DFT), the discrete cosine
transform (DCT) and the Hadamard transform (HT) enable lowpass filtering and decimation to be carried out in a single operation in the transform
domain. Size reductions of different orders are considered and the merits
of the DFT, DCT and HT are investigated.
With limited channel capacity, it is desirable to remove the
redundancy present in the source picture in order to reduce the bit
rate. Orthogonal transformation decorrelates the spatial sample
distribution and packs most of the image energy in the low order
coefficients. This property is exploited in bit-reduction schemes
which are adaptive to the local statistics of the different source
pictures used. In some cases, bit rates of less than 1.0 bit/pel
are achieved with satisfactory received picture quality.
Unlike DPCM systems, transform coding has the advantage of being
able to display rapidly a picture of low resolution by initial inverse
transformation of the low order coefficients only. Picture resolution
is then progressively built up as more coefficients are received and
decoded. Different sequences of picture update are investigated to
find that which achieves the best subjective quality with the fewest
possible coefficients transmitted
Gallium Arsenide (GaAs) Quantum Photonic Waveguide Circuits
Integrated quantum photonics is a promising approach for future practical and
large-scale quantum information processing technologies, with the prospect of
on-chip generation, manipulation and measurement of complex quantum states of
light. The gallium arsenide (GaAs) material system is a promising technology
platform, and has already successfully demonstrated key components including
waveguide integrated single-photon sources and integrated single-photon
detectors. However, quantum circuits capable of manipulating quantum states of
light have so far not been investigated in this material system. Here, we
report GaAs photonic circuits for the manipulation of single-photon and
two-photon states. Two-photon quantum interference with a visibility of 94.9
+/- 1.3% was observed in GaAs directional couplers. Classical and quantum
interference fringes with visibilities of 98.6 +/- 1.3% and 84.4 +/- 1.5%
respectively were demonstrated in Mach-Zehnder interferometers exploiting the
electro-optic Pockels effect. This work paves the way for a fully integrated
quantum technology platform based on the GaAs material system.Comment: 10 pages, 4 figure
Streaming Semidefinite Programs: Passes, Small Space and Fast Runtime
We study the problem of solving semidefinite programs (SDP) in the streaming
model. Specifically, constraint matrices and a target matrix , all of
size together with a vector are streamed to us
one-by-one. The goal is to find a matrix such
that is maximized, subject to
for all and . Previous algorithmic studies of SDP
primarily focus on \emph{time-efficiency}, and all of them require a
prohibitively large space in order to store \emph{all the
constraints}. Such space consumption is necessary for fast algorithms as it is
the size of the input. In this work, we design an interior point method (IPM)
that uses space, which is strictly sublinear in the
regime . Our algorithm takes passes, which
is standard for IPM. Moreover, when is much smaller than , our algorithm
also matches the time complexity of the state-of-the-art SDP solvers. To
achieve such a sublinear space bound, we design a novel sketching method that
enables one to compute a spectral approximation to the Hessian matrix in
space. To the best of our knowledge, this is the first method that
successfully applies sketching technique to improve SDP algorithm in terms of
space (also time)
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