13,660 research outputs found
Quantum computing through the lens of control: A tutorial introduction
Quantum computing is a fascinating interdisciplinary research field that
promises to revolutionize computing by efficiently solving previously
intractable problems. Recent years have seen tremendous progress on both the
experimental realization of quantum computing devices as well as the
development and implementation of quantum algorithms. Yet, realizing
computational advantages of quantum computers in practice remains a widely open
problem due to numerous fundamental challenges. Interestingly, many of these
challenges are connected to performance, robustness, scalability, optimization,
or feedback, all of which are central concepts in control theory. This paper
provides a tutorial introduction to quantum computing from the perspective of
control theory. We introduce the mathematical framework of quantum algorithms
ranging from basic elements including quantum bits and quantum gates to more
advanced concepts such as variational quantum algorithms and quantum errors.
The tutorial only requires basic knowledge of linear algebra and, in
particular, no prior exposure to quantum physics. Our main goal is to equip
readers with the mathematical basics required to understand and possibly solve
(control-related) problems in quantum computing. In particular, beyond the
tutorial introduction, we provide a list of research challenges in the field of
quantum computing and discuss their connections to control
Prepare for Citizen Science Challenges at CERN
Abstract:
To inspire more people to contribute to science, and educate the public about science, two Citizen Science "challenges" were prepared during summer 2013: the CERN Summer Webfest 2013 and the Virtual LHC Challenge. The first part of this report summarizes how to organize a Webfest at CERN and the outcome of the CERN Summer Webfest 2013.The second part gives an introduction to the current state of the Virtual LHC Challenge: a development of the LHC@Home Test4Theory project planned to attract many unskilled volunteers. This work was supported by a grant from the EU Citizen Cyberlab project, with assistance from the Citizen Cyberscience Centre (CCC)
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
Hidden Quantum Markov Models and Open Quantum Systems with Instantaneous Feedback
Hidden Markov Models are widely used in classical computer science to model
stochastic processes with a wide range of applications. This paper concerns the
quantum analogues of these machines --- so-called Hidden Quantum Markov Models
(HQMMs). Using the properties of Quantum Physics, HQMMs are able to generate
more complex random output sequences than their classical counterparts, even
when using the same number of internal states. They are therefore expected to
find applications as quantum simulators of stochastic processes. Here, we
emphasise that open quantum systems with instantaneous feedback are examples of
HQMMs, thereby identifying a novel application of quantum feedback control.Comment: 10 Pages, proceedings for the Interdisciplinary Symposium on Complex
Systems in Florence, September 2014, minor correction
Categorical Ontology of Complex Systems, Meta-Systems and Theory of Levels: The Emergence of Life, Human Consciousness and Society
Single cell interactomics in simpler organisms, as well as somatic cell interactomics in multicellular organisms, involve biomolecular interactions in complex signalling pathways that were recently represented in modular terms by quantum automata with âreversible behaviorâ representing normal cell cycling and division. Other implications of such quantum automata, modular modeling of signaling pathways and cell differentiation during development are in the fields of neural plasticity and brain development leading to quantum-weave dynamic patterns and specific molecular processes underlying extensive memory, learning, anticipation mechanisms and the emergence of human consciousness during the early brain development in children. Cell interactomics is here represented for the first time as a mixture of âclassicalâ states that determine molecular dynamics subject to Boltzmann statistics and âsteady-stateâ, metabolic (multi-stable) manifolds, together with âconfigurationâ spaces of metastable quantum states emerging from complex quantum dynamics of interacting networks of biomolecules, such as proteins and nucleic acids that are now collectively defined as quantum interactomics. On the other hand, the time dependent evolution over several generations of cancer cells --that are generally known to undergo frequent and extensive genetic mutations and, indeed, suffer genomic transformations at the chromosome level (such as extensive chromosomal aberrations found in many colon cancers)-- cannot be correctly represented in the âstandardâ terms of quantum automaton modules, as the normal somatic cells can. This significant difference at the cancer cell genomic level is therefore reflected in major changes in cancer cell interactomics often from one cancer cell âcycleâ to the next, and thus it requires substantial changes in the modeling strategies, mathematical tools and experimental designs aimed at understanding cancer mechanisms. Novel solutions to this important problem in carcinogenesis are proposed and experimental validation procedures are suggested. From a medical research and clinical standpoint, this approach has important consequences for addressing and preventing the development of cancer resistance to medical therapy in ongoing clinical trials involving stage III cancer patients, as well as improving the designs of future clinical trials for cancer treatments.\ud
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KEYWORDS: Emergence of Life and Human Consciousness;\ud
Proteomics; Artificial Intelligence; Complex Systems Dynamics; Quantum Automata models and Quantum Interactomics; quantum-weave dynamic patterns underlying human consciousness; specific molecular processes underlying extensive memory, learning, anticipation mechanisms and human consciousness; emergence of human consciousness during the early brain development in children; Cancer cell âcyclingâ; interacting networks of proteins and nucleic acids; genetic mutations and chromosomal aberrations in cancers, such as colon cancer; development of cancer resistance to therapy; ongoing clinical trials involving stage III cancer patientsâ possible improvements of the designs for future clinical trials and cancer treatments. \ud
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Fidelity is a sub-martingale for discrete-time quantum filters
Fidelity is known to increase through any Kraus map: the fidelity between two
density matrices is less than the fidelity between their images via a Kraus
map. We prove here that, in average, fidelity is also increasing for any
discrete-time quantum filter: fidelity between the density matrix of the
underlying Markov chain and the density matrix of its associated quantum filter
is a sub-martingale. This result is not restricted to pure states. It also
holds true for mixed states
Design of Strict Control-Lyapunov Functions for Quantum Systems with QND Measurements
We consider discrete-time quantum systems subject to Quantum Non-Demolition
(QND) measurements and controlled by an adjustable unitary evolution between
two successive QND measures. In open-loop, such QND measurements provide a
non-deterministic preparation tool exploiting the back-action of the
measurement on the quantum state. We propose here a systematic method based on
elementary graph theory and inversion of Laplacian matrices to construct strict
control-Lyapunov functions. This yields an appropriate feedback law that
stabilizes globally the system towards a chosen target state among the
open-loop stable ones, and that makes in closed-loop this preparation
deterministic. We illustrate such feedback laws through simulations
corresponding to an experimental setup with QND photon counting
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