Search results “Error correction in quantum cryptography definition”

What is QUANTUM ERROR CORRECTION? What does QUANTUM ERROR CORRECTION mean? ERROR CORRECTION definition - ERROR CORRECTION meaning - ERROR CORRECTION explanation.
Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.
Quantum error correction is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is essential if one is to achieve fault-tolerant quantum computation that can deal not only with noise on stored quantum information, but also with faulty quantum gates, faulty quantum preparation, and faulty measurements.
Classical error correction employs redundancy. The simplest way is to store the information multiple times, and—if these copies are later found to disagree—just take a majority vote; e.g. Suppose we copy a bit three times. Suppose further that a noisy error corrupts the three-bit state so that one bit is equal to zero but the other two are equal to one. If we assume that noisy errors are independent and occur with some probability p. It is most likely that the error is a single-bit error and the transmitted message is three ones. It is possible that a double-bit error occurs and the transmitted message is equal to three zeros, but this outcome is less likely than the above outcome.
Copying quantum information is not possible due to the no-cloning theorem. This theorem seems to present an obstacle to formulating a theory of quantum error correction. But it is possible to spread the information of one qubit onto a highly entangled state of several (physical) qubits. Peter Shor first discovered this method of formulating a quantum error correcting code by storing the information of one qubit onto a highly entangled state of nine qubits. A quantum error correcting code protects quantum information against errors of a limited form.
Classical error correcting codes use a syndrome measurement to diagnose which error corrupts an encoded state. We then reverse an error by applying a corrective operation based on the syndrome. Quantum error correction also employs syndrome measurements. We perform a multi-qubit measurement that does not disturb the quantum information in the encoded state but retrieves information about the error. A syndrome measurement can determine whether a qubit has been corrupted, and if so, which one. What is more, the outcome of this operation (the syndrome) tells us not only which physical qubit was affected, but also, in which of several possible ways it was affected. The latter is counter-intuitive at first sight: Since noise is arbitrary, how can the effect of noise be one of only few distinct possibilities? In most codes, the effect is either a bit flip, or a sign (of the phase) flip, or both (corresponding to the Pauli matrices X, Z, and Y). The reason is that the measurement of the syndrome has the projective effect of a quantum measurement. So even if the error due to the noise was arbitrary, it can be expressed as a superposition of basis operations—the error basis (which is here given by the Pauli matrices and the identity). The syndrome measurement "forces" the qubit to "decide" for a certain specific "Pauli error" to "have happened", and the syndrome tells us which, so that we can let the same Pauli operator act again on the corrupted qubit to revert the effect of the error.
The syndrome measurement tells us as much as possible about the error that has happened, but nothing at all about the value that is stored in the logical qubit—as otherwise the measurement would destroy any quantum superposition of this logical qubit with other qubits in the quantum computer.

Views: 879
The Audiopedia

Dr. Daniel Gottesman, Research Scientist at the Perimeter Institute for Theoretical Physics, gave a lecture about Quantum Error Correction and Fault Tolerance.
The lecture is the second of two parts, and was filmed at the Canadian Summer School on Quantum Information, held at the University of Waterloo in June of 2012.
For More:
http://iqc.uwaterloo.ca
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QuantumFactory Blog: http://quantumfactory.wordpress.com

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Institute for Quantum Computing

Daniel Gottesman, Perimeter Institute
Quantum Hamiltonian Complexity Reunion Workshop
http://simons.berkeley.edu/talks/daniel-gottesman-2015-05-08

Views: 901
Simons Institute

A talk by Daniel Gottesman at the 4th International Conference on Quantum Error Correction, hosted September 11-15, 2017 by Georgia Tech and the Joint Center for Quantum Information and Computer Science at the University of Maryland.

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QuICS

Where are the limits of human technology? And can we somehow avoid them? This is where quantum computers become very interesting.
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Quantum Computers Explained – Limits of Human Technology
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Kurzgesagt – In a Nutshell

What is Information? - Part 2a - Introduction to Information Theory:
Script: http://crackingthenutshell.org/what-is-information-part-2a-information-theory
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- Claude Shannon - Bell Labs - Father of Information Theory
- A Mathematical Theory of Communication - 1948
- Book, co-written with Warren Weaver
- How to transmit information efficiently, reliably & securely through a given channel (e.g. tackling evesdropping)
- Applications. Lossless data compression (ZIP files). Lossy data compression (MP3, JPG). Cryptography, thermal physics, quantum computing, neurobiology
- Shannon's definition not related to meaningfulness, value or other qualitative properties - theory tackles practical issues
- Shannon's information, a purely quantitative measure of communication exchanges
- Shannon's Entropy. John von Neumann. Shannon's information, information entropy - avoid confusion with with thermodynamical entropy
- Shannon's Entropy formula. H as the negative of a certain sum involving probabilities
- Examples: fair coin & two-headed coin
- Information gain = uncertainty reduction in the receiver's knowledge
- Shannon's entropy as missing information, lack of information
- Estimating the entropy per character of the written English language
- Constraints such as "I before E except after C" reduce H per symbol
- Taking into account redundancy & contextuality
- Redundancy, predictability, entropy per character, compressibility
- What is data compression? - Extracting redundancy
- Source Coding Theorem. Entropy as a lower limit for lossless data compression.
- ASCII codes
- Example using Huffman code. David Huffman. Variable length coding
- Other compression techniques: arithmetic coding
- Quality vs Quantity of information
- John Tukey's bit vs Shannon's bit
- Difference between storage bit & information content. Encoded data vs Shannon's information
- Coming in the next video: error correction and detection, Noisy-channel coding theorem, error-correcting codes, Hamming codes, James Gates discovery, the laws of physics, How does Nature store Information, biology, DNA, cosmological & biological evolution

Views: 54330
Cracking The Nutshell

What is INFORMATION THEORY? What does INFORMATION THEORY mean? INFORMATION THEORY meaning.
Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.
Information theory studies the quantification, storage, and communication of information. It was originally proposed by Claude E. Shannon in 1948 to find fundamental limits on signal processing and communication operations such as data compression, in a landmark paper entitled "A Mathematical Theory of Communication". Now this theory has found applications in many other areas, including statistical inference, natural language processing, cryptography, neurobiology, the evolution and function of molecular codes, model selection in ecology, thermal physics, quantum computing, linguistics, plagiarism detection, pattern recognition, and anomaly detection.
A key measure in information theory is "entropy". Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a die (with six equally likely outcomes). Some other important measures in information theory are mutual information, channel capacity, error exponents, and relative entropy.
Applications of fundamental topics of information theory include lossless data compression (e.g. ZIP files), lossy data compression (e.g. MP3s and JPEGs), and channel coding (e.g. for Digital Subscriber Line (DSL)).
The field is at the intersection of mathematics, statistics, computer science, physics, neurobiology, and electrical engineering. Its impact has been crucial to the success of the Voyager missions to deep space, the invention of the compact disc, the feasibility of mobile phones, the development of the Internet, the study of linguistics and of human perception, the understanding of black holes, and numerous other fields. Important sub-fields of information theory include source coding, channel coding, algorithmic complexity theory, algorithmic information theory, information-theoretic security, and measures of information.
Information theory studies the transmission, processing, utilization, and extraction of information. Abstractly, information can be thought of as the resolution of uncertainty. In the case of communication of information over a noisy channel, this abstract concept was made concrete in 1948 by Claude Shannon in his paper "A Mathematical Theory of Communication", in which "information" is thought of as a set of possible messages, where the goal is to send these messages over a noisy channel, and then to have the receiver reconstruct the message with low probability of error, in spite of the channel noise. Shannon's main result, the noisy-channel coding theorem showed that, in the limit of many channel uses, the rate of information that is asymptotically achievable is equal to the channel capacity, a quantity dependent merely on the statistics of the channel over which the messages are sent.
Information theory is closely associated with a collection of pure and applied disciplines that have been investigated and reduced to engineering practice under a variety of rubrics throughout the world over the past half century or more: adaptive systems, anticipatory systems, artificial intelligence, complex systems, complexity science, cybernetics, informatics, machine learning, along with systems sciences of many descriptions. Information theory is a broad and deep mathematical theory, with equally broad and deep applications, amongst which is the vital field of coding theory.
Coding theory is concerned with finding explicit methods, called codes, for increasing the efficiency and reducing the error rate of data communication over noisy channels to near the Channel capacity. These codes can be roughly subdivided into data compression (source coding) and error-correction (channel coding) techniques. In the latter case, it took many years to find the methods Shannon's work proved were possible. A third class of information theory codes are cryptographic algorithms (both codes and ciphers). Concepts, methods and results from coding theory and information theory are widely used in cryptography and cryptanalysis. See the article ban (unit) for a historical application.
Information theory is also used in information retrieval, intelligence gathering, gambling, statistics, and even in musical composition.

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The Audiopedia

Security+ Training Course Index: http://professormesser.link/sy0501
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Professor Messer

This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.

Views: 2687
Udacity

Lecture title: "The Growth of Cryptography"
Ronald L. Rivest, a professor of electrical engineering and computer science who helped develop one of the world's most widely used Internet security systems, was MIT’s James R. Killian, Jr. Faculty Achievement Award winner for 2010–2011. Rivest, the Andrew and Erna Viterbi professor in MIT's Department of Electrical Engineering and Computer Science, is known for his pioneering work in the field of cryptography, computer, and network security.
February 8, 2011
Huntington Hall (10-250)

Views: 618
MIT Institute Events

Views: 214
Ahmed Suleiman

The discovery of quantum error correction and fault-tolerance were major theoretical breakthroughs on the road towards building a full-fledged quantum computer. Since then thresholds have increased and geometric constraints on the underlying architecture have been added. Homological stabilizer codes provide a method for constructing stabilizer codes constrained to a 2D plane. In this talk I will define and proceed to classify all 2D homological stabilizer codes. I will show that Kitaev's toric code and the topological color codes arise naturally in this classification. I will finally show, up to a set of equivalence relations, that these are the only 2D homological stabilizer codes.

Views: 181
Microsoft Research

Claude Shannon's idea of perfect secrecy: no amount of computational power can help improve your ability to break the one-time pad
Watch the next lesson: https://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/random-vs-pseudorandom-number-generators?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience
Missed the previous lesson? https://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/case-study-ww2-encryption-machines?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience
Computer Science on Khan Academy: Learn select topics from computer science - algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we encode and compress information).
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
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Khan Academy Labs

John Preskill, Richard P. Feynman Professor of Theoretical Physics at the California Institute of Technology, gave a lecture about Introduction to Quantum Information.
The lecture is the first of two parts, and was filmed at the Canadian Summer School on Quantum Information, held at the University of Waterloo in June of 2012.
Find out more about IQC!
Website - https://uwaterloo.ca/institute-for-quantum-computing/
Facebook - https://www.facebook.com/QuantumIQC
Twitter - https://twitter.com/QuantumIQC

Views: 38395
Institute for Quantum Computing

John Martinis visited Google LA to give a tech talk: "Design of a Superconducting Quantum Computer." This talk took place on October 15, 2013.
Bio:
John M. Martinis attended the University of California at Berkeley from 1976 to 1987, where he received two degrees in Physics: B.S. (1980) and Ph.D. (1987). His thesis research focused on macroscopic quantum tunneling in Josephson Junctions. After completing a post-doctoral position at the Commisiariat Energie Atomic in Saclay, France, he joined the Electromagnetic Technology division at NIST in Boulder. At NIST he was involved in understanding the basic physics of the Coulomb Blockade, and worked to use this phenomenon to make a new fundamental electrical standard based on counting electrons. While at NIST he also invented microcalorimeters based on superconducting sensors for x-ray microanalysis and astrophysics. In June of 2004 he moved to the University of California, Santa Barbara where he currently holds the Worster Chair. At UCSB, he has continued work on quantum computation. Along with Andrew Cleland, he was awarded in 2010 the AAAS science breakthrough of the year for work showing quantum behavior of a mechanical oscillator.
Abstract:
Superconducting quantum computing is now at an important crossroad, where "proof of concept" experiments involving small numbers of qubits can be transitioned to more challenging and systematic approaches that could actually lead to building a quantum computer. Our optimism is based on two recent developments: a new hardware architecture for error detection based on "surface codes" [1], and recent improvements in the coherence of superconducting qubits [2]. I will explain how the surface code is a major advance for quantum computing, as it allows one to use qubits with realistic fidelities, and has a connection architecture that is compatible with integrated circuit technology. Additionally, the surface code allows quantum error detection to be understood using simple principles. I will also discuss how the hardware characteristics of superconducting qubits map into this architecture, and review recent results that suggest gate errors can be reduced to below that needed for the error detection threshold.
References
[1] Austin G. Fowler, Matteo Mariantoni, John M. Martinis and Andrew N. Cleland, PRA 86, 032324 (2012).
[2] R. Barends, J. Kelly, A. Megrant, D. Sank, E. Jeffrey, Y. Chen, Y. Yin, B. Chiaro, J. Mutus, C. Neill, P. O'Malley, P. Roushan, J. Wenner, T. C. White, A. N. Cleland and John M. Martinis, arXiv:1304:2322.

Views: 60674
GoogleTechTalks

This talk discards hand-wavy pop-science metaphors and answers a simple question: from a computer science perspective, how can a quantum computer outperform a classical computer? Attendees will learn the following:
- Representing computation with basic linear algebra (matrices and vectors)
- The computational workings of qbits, superposition, and quantum logic gates
- Solving the Deutsch oracle problem: the simplest problem where a quantum computer outperforms classical methods
- Bonus topics: quantum entanglement and teleportation
The talk concludes with a live demonstration of quantum entanglement on a real-world quantum computer, and a demo of the Deutsch oracle problem implemented in Q# with the Microsoft Quantum Development Kit. This talk assumes no prerequisite knowledge, although comfort with basic linear algebra (matrices, vectors, matrix multiplication) will ease understanding.
See more at https://www.microsoft.com/en-us/research/video/quantum-computing-computer-scientists/

Views: 58546
Microsoft Research

Prof. Shoucheng Zhang discusses three pillars of information technology: quantum computing, AI and blockchain. He presents the fundamentals of crypto-economic science, and answers questions such as: What is the intrinsic value of a medium of exchange? What is the value of consensus and how does it emerge? How can math be used to create distributed self-organizing consensus networks to create a data-marketplace for AI and machine learning?
Prof. Zhang is the JG Jackson and CJ Wood professor of physics at Stanford University. He is a member of the US National Academy of Science, the American Academy of Arts and Sciences and a foreign member of the Chinese Academy of Sciences. He discovered a new state of matter called topological insulator in which electrons can conduct along the edge without dissipation, enabling a new generation of electronic devices with much lower power consumption. For this ground breaking work he received numerous international awards, including the Buckley Prize, the Dirac Medal and Prize, the Europhysics Prize, the Physics Frontiers Prize and the Benjamin Franklin Medal.
He is also the founding chairman of DHVC venture capital fund, which invests in AI, blockchain, mobile internet, big data, AR/VR, genomics and precision medicine, sharing economy and robotics.

Views: 12563
Talks at Google

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The science of information is the most influential, yet perhaps least appreciated field in science today. Never before in history have we been able to acquire, record, communicate, and use information in so many different forms. Never before have we had access to such vast quantities of data of every kind. This revolution goes far beyond the limitless content that fills our lives, because information also underlies our understanding of ourselves, the natural world, and the universe. It is the key that unites fields as different as linguistics, cryptography, neuroscience, genetics, economics, and quantum mechanics. And the fact that information bears no necessary connection to meaning makes it a profound puzzle that people with a passion for philosophy have pondered for centuries.
Little wonder that an entirely new science has arisen that is devoted to deepening our understanding of information and our ability to use it. Called information theory, this field has been responsible for path-breaking insights such as the following:
What is information? In 1948, mathematician Claude Shannon boldly captured the essence of information with a definition that doesn’t invoke abstract concepts such as meaning or knowledge. In Shannon’s revolutionary view, information is simply the ability to distinguish reliably among possible alternatives.
The bit: Atomic theory has the atom. Information theory has the bit: the basic unit of information. Proposed by Shannon’s colleague at Bell Labs, John Tukey, bit stands for “binary digit”—0 or 1 in binary notation, which can be implemented with a simple on/off switch. Everything from books to black holes can be measured in bits.
Redundancy: Redundancy in information may seem like mere inefficiency, but it is a crucial feature of information of all types, including languages and DNA, since it provides built-in error correction for mistakes and noise. Redundancy is also the key to breaking secret codes.
Building on these and other fundamental principles, information theory spawned the digital revolution of today, just as the discoveries of Galileo and Newton laid the foundation for the scientific revolution four centuries ago. Technologies for computing, telecommunication, and encryption are now common, and it’s easy to forget that these powerful technologies and techniques had their own Galileos and Newtons.
The Science of Information: From Language to Black Holes covers the exciting concepts, history, and applications of information theory in 24 challenging and eye-opening half-hour lectures taught by Professor Benjamin Schumacher of Kenyon College. A prominent physicist and award-winning educator at one of the nation’s top liberal arts colleges, Professor Schumacher is also a pioneer in the field of quantum information, which is the latest exciting development in this dynamic scientific field.
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Views: 1706
The Great Courses Plus

Encryption key distribution is a fundamental cryptographic research area. In this work, we present a one-pass key distribution protocol utilizing the Hamming Error Detection and Correction Code. The shared secret is a random string of bits. For high-security applications, this shared secret can be changed for generating a new key. For other types of applications, we show that this step is nonobligatory since the bit string is partially updated every time a new key is generated. Additionally, the Strict Avalanche Criteria (SAC) of any hash function design results in a change of 50% of the output bits for a one-bit change in the input to the hash function. Therefore, the shared secret is acquired only one time as an initial value (IV). It also serves as an authentication vehicle. The proposed technique uses simple arithmetic and logic operations that provide uncomplicated and efficient software and hardware implementations.

Views: 193
Magdy Saeb

Helger Lipmaa (Tartu Universitāte) referāts "Succinct Non-Interactive Zero Knowledge Arguments from Span Programs and Linear Error-Correcting Codes",
Recently, Gennaro, Gentry, Parno and Raykova [GGPR12] proposed an ecient non-interactive zero knowledge argument for Circuit-SAT, based on non-standard notions like conscientious and quadratic span programs. We propose a new non-interactive zero knowledge argument, based on a simple combination of standard span programs (that verify the correctness of every individual gate) and high-distance linear error-correcting codes (that check the consistency of wire assignments). We simplify all steps of the argument. As one of the corollaries, we design an (optimal) wire checker, based on systematic Reed-Solomon codes, of size 8n and degree 4n, while the wire checker from [GGPR12] has size 24n and degree 76n, where n is the circuit size. Importantly, the new argument has constant verier's computation.
(publikācija: http://eprint.iacr.org/2013/121)
Kvantu un kritpo diena 2013 (Quantum and Crypto Day 2013) Latvijas Universitātes Datorikas fakultātē notika 2013. gada 25. aprīlī. Plašāka informācija: http://www.df.lu.lv/zinas/t/20343/

Views: 910
Latvijas Universitāte

What does qudit mean?
A spoken definition of qudit.
Intro Sound:
Typewriter - Tamskp
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Groove Groove - Kevin MacLeod (incompetech.com)
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The best days are not planned - Marcus Hansson
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What Does That Mean?

The field of computer science summarised. Learn more at this video's sponsor https://brilliant.org/dos
Computer science is the subject that studies what computers can do and investigates the best ways you can solve the problems of the world with them. It is a huge field overlapping pure mathematics, engineering and many other scientific disciplines. In this video I summarise as much of the subject as I can and show how the areas are related to each other.
A couple of notes on this video:
1. Some people have commented that I should have included computer security alongside hacking, and I completely agree, that was an oversight on my part. Apologies to all the computer security professionals, and thanks for all the hard work!
2. I also failed to mention interpreters alongside compilers in the complier section. Again, I’m kicking myself because of course this is an important concept for people to hear about. Also the layers of languages being compiled to other languages is overly convoluted, in practice it is more simple than this. I guess I should have picked one simple example.
3. NP-complete problems are possible to solve, they just become very difficult to solve very quickly as they get bigger. When I said NP-complete and then "impossible to solve", I meant that the large NP-complete problems that industry is interested in solving were thought to be practically impossible to solve.
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Domain of Science

Fabian Furrer of Institut für Theoretische Physik, Universität Hannover and the University of Tokyo presented: Continuous variable entropic uncertainty relations in the presence of quantum memory on behalf of his co-authors Mario Berta (Institut für Theoretische Physik, ETH Zürich), Matthias Christandl (Institut für Theoretische Physik, ETH Zürich), Volkher Schultz (Institut für Theoretische Physik, ETH Zürich) and Marco Tomamichel (Centre for Quantum Technologies, National University of Singapore) at the 2013 QCrypt Conference in August. http://2013.qcrypt.net
Find out more about IQC!
Website - https://uwaterloo.ca/institute-for-quantum-computing/
Facebook - https://www.facebook.com/QuantumIQC
Twitter - https://twitter.com/QuantumIQC

Views: 424
Institute for Quantum Computing

Claude Elwood Shannon, father of the information age, was born 100 years ago, on April 30th, 1916. He defined the entropy of information, coined the term “bit”, and laid the foundations of the communication networks we have today.
http://www.itsoc.org/resources/Shannon-Centenary
https://en.wikipedia.org/wiki/Claude_Shannon#Shannon_Centenary

Views: 10578
IEEE Information Theory Society

What is a quantum computer and what is quantum computing?
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Full agenda below!
https://eestalktech.com/what-is-quantum-computing
Twitter: @Keysight_Daniel https://twitter.com/Keysight_Daniel
Learn more about using oscilloscopes:
http://oscilloscopelearningcenter.com
Check out the EEs Talk Tech electrical engineering podcast:
https://eestalktech.com
The 2-Minute Guru Season 2 playlist:
https://www.youtube.com/playlist?list=PLzHyxysSubUlqBguuVZCeNn47GSK8rcso
More about Keysight oscilloscopes:
http://bit.ly/SCOPES
Check out our blog:
http://bit.ly/ScopesBlog
Agenda:
0:45 Intro
Lee Barford's job is to help to guide Keysight into the quantum computing industry and enable quantum computing experts
2:00 Why is quantum computing/a quantum computer important?
Clock rates for digital processors stopped getting faster around 2006 because of excessive heat
The processor manufacturers realized they needed more processor parallelism
Graphics processor units (GPUs) can be used as vector and matrix computational machines
Bitcoin utilizes this method.
6:00 What does the development of quantum computing and quantum computers mean for the future?
Gates being made with feature size of the digital transistor that have an effective gate length of down to 7 nm
Now we're pushing below 5 nm, and there are not many unit cells of silicon left in the layer. (one unit cell of silicon is 0.5 nanometer)
The Heisenberg uncertainty principle comes into play at this point because there are few enough atoms that quantum mechanical effects will disturb electronics.
These quantum mechanical effects include a superposition of states (Schrodinger's cat) and low error tolerance.
10:20 When will Moore's law fail?
Quantum computing and quantum computers are one way of moving the computing industry past this barrier by taking advantage of quantum effects - engineering with them - to build a quantum computer that will do certain tasks much faster than today's computers.
15:20 Questions for future episodes:
What sort of technology does it take to make a quantum computer?
Where are current experiments probing?
Why are people funding quantum computing research and the building of quantum computers?
What problems are quantum computing (and quantum computers) working to solve?
17:30 Using quantum effects
Quantum computers probably won't be used in consumer devices because it currently requires a very low temperature and/or a vacuum.
18:00 The quantum computer's fundamental storage unit is a qubit (quantum bit). It can be in states 1 or 0 with some finite probability
19:00
You can set up a quantum register to store multiple potential qubits, and when read out, have an identical probability to be either of these numbers. A quantum register can store multiple states at once, but only one register value can be read out of the quantum register.
21:00 How do you get the desired value out of a quantum register? You do as much of the computation ahead of time and then read the quantum computers quantum register.
It works because the answer is either such a high probability to be correct that you don't need to check it, or it is very easy to double check if the answer is correct.
21:00 How do you get the desired value out of a quantum register? You do as much of the computation ahead of time and then read the quantum computers quantum register.
22:30 Quantum computers are good at factoring very large numbers (breaking RSA in cryptography)
#oscilloscope #oscilloscopes #electronics #electricalengineering

Views: 1400
Keysight Labs

WW2 Encryption is explored with a focus on the Enigma. Read more here.
Watch the next lesson: https://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/perfect-secrecy?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience
Missed the previous lesson? https://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/frequency-stability?utm_source=YT&utm_medium=Desc&utm_campaign=computerscience
Computer Science on Khan Academy: Learn select topics from computer science - algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we encode and compress information).
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Computer Science channel: https://www.youtube.com/channel/UC8uHgAVBOy5h1fDsjQghWCw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 185223
Khan Academy Labs

Daniel Lidar visited the Quantum AI Lab at Google LA to give a talk: "Quantum Information Processing: Are We There Yet?" This talk took place on January 22, 2015.
Abstract:
Quantum information processing holds great promise, yet large-scale, general purpose quantum computers capable of solving hard problems are not yet available despite 20+ years of immense effort. In this talk I will describe some of this promise and effort, as well as the obstacles and ideas for overcoming them using error correction techniques. I will focus on a special purpose quantum information processor called a quantum annealer, designed to speed up the solution to tough optimization problems. In October 2011 USC and Lockheed-Martin jointly founded a quantum computing center housing a commercial quantum annealer built by the Canadian company D-Wave Systems. A similar device is operated by NASA and Google. These processors use superconducting flux qubits to minimize the energy of classical spin-glass models with as many spins as qubits, an NP-hard problem with numerous applications. There has been much controversy surrounding the D-Wave processors, questioning whether they offer any advantage over classical computing. I will survey the recent work we have done to benchmark the processors against highly optimized classical algorithms, to test for quantum effects, and to perform error correction.
Bio:
Daniel Lidar has worked in quantum computing for nearly 20 years. He is a professor of electrical engineering, chemistry, and physics at USC, and hold a Ph.D. in physics from the Hebrew University of Jerusalem. His work revolves around various aspects of quantum information science, including quantum algorithms, quantum control, the theory of open quantum systems, and theoretical as well as experimental adiabatic quantum computation. He is a Fellow of the AAAS, APS, and IEEE. Lidar is the Director of the USC Center for Quantum Information Science and Technology, and is the Scientific Director of the USC-Lockheed Martin Center for Quantum Computing. Two of his former graduate students are now research scientists at Google’s quantum artificial intelligence lab.

Views: 13603
GoogleTechTalks

Welcome to my new reinforcement learning course! For the next 10 weeks we're going to go from the basics to the state of the art in this popular subfield of machine learning using video game environments as our testbed. RL is a huge reason DeepMind and OpenAI have been so successful thus far in creating world changing AI bots. Make sure to subscribe so you'll get updated with every new video I release. And don't worry if you don't understand policy iteration or value iteration just yet, I merely wanted to introduce these phrases in this video, next week i'm going to really dive into what these 2 methods look like programmatically.
Code for this video (with coding challenge):
https://github.com/llSourcell/AI_for_video_games_demo
Syllabus for this course:
https://github.com/llSourcell/AI_for_Video_Games_Syllabus
Please Subscribe! And like. And comment. That's what keeps me going.
Want more inspiration & education? Follow me:
Twitter: https://twitter.com/sirajraval
Facebook: https://www.facebook.com/sirajology
More learning resources:
https://medium.com/emergent-future/simple-reinforcement-learning-with-tensorflow-part-0-q-learning-with-tables-and-neural-networks-d195264329d0
http://icml.cc/2016/tutorials/deep_rl_tutorial.pdf
https://github.com/MorvanZhou/Reinforcement-learning-with-tensorflow
https://www.analyticsvidhya.com/blog/2017/01/introduction-to-reinforcement-learning-implementation/
https://web.mst.edu/~gosavia/tutorial.pdf
http://karpathy.github.io/2016/05/31/rl/
http://www.wildml.com/2016/10/learning-reinforcement-learning/
https://www.quora.com/What-are-some-good-tutorials-on-reinforcement-learning
Join us in the Wizards Slack channel:
http://wizards.herokuapp.com/
And please support me on Patreon:
https://www.patreon.com/user?u=3191693 Instagram: https://www.instagram.com/sirajraval/ Instagram: https://www.instagram.com/sirajraval/

Views: 38931
Siraj Raval

Perry Marshall, Author of "Industrial Ethernet" and Communications Engineer Bill Jenkins give a technical Treatment of Information Theory as it relates to DNA and Evolution. The structure of DNA and why it is by definition a code.

Views: 4719
Evolution 2.0

what the science
Quantum computer, another sci-fi word or the future reality....watch to find out
The first computer was made in the year 1949. Which was called ENIC, electronic numerical integrator and computer. It was so huge that it took an entire floor or two, and at the same time, it was very slow and less powerful as compared to the modern-day computers.
But as the time went by computers had become smaller and smarter, this reduction of size will continue and soon the Morden day computers will reach its physical limit. Here is where quantum computers come in, These computers will be extremely powerful
and will also help to create smaller and more powerful computers.
Please do like share and subscribe.
Subscribe: https://www.youtube.com/channel/UClFHOffx2_DpPHNz2WdvQsA
Facebook page: https://www.facebook.com/wtsavk/
Twitter: https://twitter.com/wts_avk

Views: 429
What The Science

Das wohl wichtigste ungelöste Problem der Mathematik.
* Weihnachtsvorlesung 2017 (mehrere Teile) ab hier: http://weitz.de/y/TOcQ_jIYQwo?list=PLb0zKSynM2PAuxxtMK1bxYPV_bUoPtpTB
* "Alternative" Weihnachtsvorlesung 2017: http://weitz.de/y/Vv3Rve3yXBY?list=PLb0zKSynM2PAuxxtMK1bxYPV_bUoPtpTB
* Weihnachtsvorlesung 2015: http://weitz.de/y/q2iZDtotiM0?list=PLb0zKSynM2PAuxxtMK1bxYPV_bUoPtpTB
* Weihnachtsvorlesung 2014 (mehrere Teile) ab hier: http://weitz.de/y/40Mt9WdSNEk?list=PLb0zKSynM2PAuxxtMK1bxYPV_bUoPtpTB
* Weihnachtsvorlesung 2013 (mehrere Teile) ab hier: http://weitz.de/y/2w1_kWn-F0s?list=PLb0zKSynM2PAuxxtMK1bxYPV_bUoPtpTB
* "Sommervorlesung" 2014: http://weitz.de/y/BNx0ObN6fVc?list=PLb0zKSynM2PAuxxtMK1bxYPV_bUoPtpTB
Da dieser Vortrag, der ursprünglich vor nur etwa fünfzig Zuhörern gehalten wurde, inzwischen zu meiner Überraschung auf YouTube äußerst populär geworden ist, muss ich doch mal etwas klarstellen: Es handelt sich hier nicht um eine Vorlesung für Mathematiker, sondern um einen einmaligen "populärwissenschaftlichen" Vortrag, der sich an ein bunt gemischtes Publikum richtete; darunter auch viele "Laien", die nur Schulwissen der Mathematik mitbrachten (und das wahrscheinlich auch schon vergessen hatten). Es ging darum, Zuhörern, die sonst nichts mit Mathe am Hut haben, anhand eines Beispiels eine Vorstellung davon zu vermitteln, welche Fragen Mathematiker eigentlich beschäftigen.
Allgemeine Anmerkungen: http://weitz.de/youtube.html

Views: 386303
Weitz / HAW Hamburg

What is the essence of information? We explore the history of communication technology leading to the modern field of information theory. We'll build up towards Claude Shannon's measure of information entropy, one step at a time.

Views: 190714
Art of the Problem

Dr. Virgil Gligor, Professor of Electrical and Computer Engineering, Carnegie Mellon and Cylab, presents "On the Fragiliity of Adversary Definitions in Cryptographic Protocols" on November 6, 2008. Note: Original video was 320x240.

Views: 324
Rutgers University

Moore's Law -- putting more and more transistors on a chip -- accelerated the computing industry by so many orders of magnitude, it has (and continues to) achieve seemingly impossible feats. However, we're now resorting to brute-force hacks to keep pushing it beyond its limits and are getting closer to the point of diminishing returns (especially given costly manufacturing infrastructure). Yet this very dynamic is leading to "a Cambrian explosion" in computing capabilities… just look at what's happening today with GPUs, FPGAs, and neuromorphic chips. Through such continuing performance improvements and parallelization, classic computing continues to reshape the modern world.
But we're so focused on making our computers do more that we're not talking enough about what classic computers can't do -- and that's to compute things the way nature does, which operates in quantum mechanics. So our smart machines are really quite dumb, argues Rigetti Computing founder and CEO Chad Rigetti; they're limited to human-made binary code vs. the natural reality of continuous variables. This in turn limits our ability to work on problems that classic computers can't solve, such as key applications in computational chemistry or large-scale optimization for machine learning and artificial intelligence. Which is where quantum computing comes in.
SUBCRIBE - https://goo.gl/aiECKP
The a16z Podcast discusses tech and culture trends, news, and the future -- especially as ‘software eats the world’. It features industry experts, business leaders, and other interesting thinkers and voices from around the world. This podcast is produced by Andreessen Horowitz (aka “a16z”), a Silicon Valley-based venture capital firm. Multiple episodes are released every week; visit a16z.com for more details.

Views: 193
a16z - Andreessen Horowitz

How do you stack hundred-dimensional oranges? Learn about recent breakthroughs in our understanding of hyperspheres in the first episode of Infinite Series, a show that tackles the mysteries and the joy of mathematics. From Logic to Calculus, from Probability to Projective Geometry, Infinite Series both entertains and challenges its viewers to take their math game to the next level.
Higher dimensional spheres, or hyperspheres, are counter-intuitive and almost impossible to visualize. Mathematician Kelsey Houston-Edwards explains higher dimensional spheres and how recent revelations in sphere packing have exposed truths about 8 and 24 dimensions that we don't even understand in 4 dimensions.
Tweet at us! @pbsinfinite
Facebook: facebook.com/pbsinfinite series
Email us! pbsinfiniteseries [at] gmail [dot] com
Sphere Packing in Higher Dimensions - Quanta Magazine
https://www.quantamagazine.org/20160330-sphere-packing-solved-in-higher-dimensions/
Why You Should Care about High-Dimensional Sphere Packing - Scientific American
https://blogs.scientificamerican.com/roots-of-unity/why-you-should-care-about-high-dimensional-sphere-packing/
Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux
Made by Kornhaber Brown (www.kornhaberbrown.com)

Views: 677177
PBS Infinite Series

How many queries are needed to determine a polynomial F(X)? We look at this question when F(X) is defined over a finite field GF(q) and has degree d, such that d+1 queries are obviously sufficient. Shamir's Secret Sharing protocol is based on the result that d+1 classical queries are also needed as no interpolation is possible based on only d values of F. Here we look at how many quantum queries are sufficient to perform the same task. Earlier work by [Kane & Kutin 2009] and [Meyer & Pommersheim 2010] proved that at least d/2+1/2 quantum queries are needed, while [Boneh and Zhandry 2012] showed that d quantum queries are sufficient. In this talk we will describe a quantum algorithm that uses only d/2+1/2 queries and that has a constant success probability. Our algorithm relies on the analysis of the classical Moment Problem defined over finite fields. (Joint work with Andrew Childs)

Views: 121
Microsoft Research

Steven Chu (b. 1948) served as secretary of the United States Department of Energy from 2009 to 2013 and was co-winner of the 1997 Nobel Prize for Physics for his work in methods to cool and trap atoms with laser light.
Dr. Chu was born in St. Louis, Missouri, into a family of scholars who placed an enormous value on education. Both his father and mother studied at MIT, in chemical engineering and economics, respectively, and they nurtured intellectual curiosity in their children. As a young child, Dr. Chu built model airplanes and warships, graduated to Erector Sets, and later, spent his school lunch money on parts for homemade rockets that he constructed with a friend. He matriculated to the University of Rochester, where he developed a love for physics and mathematics, and from which he graduated in 1970. In 1976, after completing his graduate and postdoctoral work at the University of California at Berkeley, Dr. Chu spent nine years at Bell Laboratories. The atmosphere at Bell Labs during that period (1978–1987) was one “permeated by the joy and excitement of doing science,” according to Dr. Chu, and his work there led to the laser cooling and trapping of atoms for which he was awarded the Nobel Prize.
In 1987, Dr. Chu returned to California as professor of physics and applied physics at Stanford University, where he taught until 2009. From 2004–2009, he directed the Lawrence Berkeley National Laboratory (a US Department of Energy laboratory operated by the University of California) while continuing to teach physics at Stanford.
Dr. Chu’s appointment to the Cabinet recognized his commitment to addressing energy challenges of all types, including energy efficiency, greenhouse gas emissions, and the nation’s dependence on foreign oil. As secretary, Dr. Chu was dedicated to supporting companies that are working to refine existing green technologies (such as better batteries for plug-in hybrids and electric vehicles) and to moving those technologies into the marketplace.
Learn more about Steven Chu through the US Department of Energy or via his autobiography on the Nobel Prize website.

Views: 597
MIT Video Productions External

Views: 3535
Project Rhea

If you like this video and want to support me, go this page for my donation crypto addresses:
https://www.youtube.com/c/mobilefish/about
This is part 9 of the IOTA tutorial.
In this video series different topics will be explained which will help you to understand IOTA.
It is recommended to watch each video sequentially as I may refer to certain IOTA topics explained earlier.
The procedure to generate IOTA addresses is as follows:
IOTA addresses are deterministically generated starting with the seed (81 trytes).
Seed (trytes): C9RQF ... QIAWT
Convert the seed (81 trytes) to trits (= 81 x 3 = 243 trits)
Seed (trits): 0,1,0,0,0,0 ... -1,-1,0,-1,1,-1
Every address has a corresponding key index number.
A key index number is an integer starting from 0.
Address 0 has key index number 0, address 1 has key index number 1, etc.
They key index number always starts with integer 0, and is simply incremented in order to get the next address.
The largest key index number allowed is 9007199254740991.
This largest key index number is the same as 2^53 - 1, which is the same as the Javascript constant: Number.MAX_SAFE_INTEGER
An IOTA seed can generate in total 9007199254740992 addresses.
The decimal key index number must be converted to trits.
For example the key index number 1 converted to trits looks like: 1,0,0
Next create a subseed by adding the key index number and seed together.
subseed = seed + key index number
IOTA provides 3 security levels: 1, 2 or 3.
A security level determines the number of rounds for hashing, which means that a single seed can have 3 different accounts.
A different security level with the same index number, means that you will get a different address.
Security level 1, Key size (trits): 6561 x 1
Remark: Used for low security (for very high efficiency). Best for tiny IoT devices that only transact/store small amounts of value.
Security level 2, Key size (trits): 6561 x 2
Remark: Used for standard security (for medium performance). Best for regular people's wallets and devices that store higher amounts of value.
Security level 3, Key size (trits): 6561 x 4
Remark: Used for full blown quantum proof security that conforms to National Security Agency’s (NSA) recommendations for sensitive material.
Good for big value transactions and paranoids.
Client libraries, such as iota.lib.js makes it possible to choose another security level.
See: https://www.mobilefish.com/services/cryptocurrency/iota_wallet.html
By default the IOTA light wallet uses security level 2 and you can not change its security level.
If you created an address using security level 1 or 3 this address will not appear in the IOTA light wallet using the same seed.
In the next slide a simplistic explanation is given how the subseed is hashed multiple times using the Keccak-384 hash algorithm.
The hashing is done in a wrapper class called Kerl.
The seed and subseed can differ between the first 1 tryte up to and including 12 trytes.
If someone else has exactly the last 69 (= 81 - 12) trytes up to and including 81 trytes of your seed they can see the balance of one or more of your addresses.
The probability that someone else happens to have the same last 69 trytes of your seed is very small.
Here is the proof: IOTA seed with only 69 trytes has 27^69 = 5.80 x 10^98 possible combinations.
For comparison: A Bitcoin private key with 256 bits has 2^256 = 1.15 x 10^77 possible combinations.
This means, even if you have an IOTA seed with only 69 trytes it has more possible combinations than a Bitcoin private key.
A checksum is an additional 9 trytes added to an address (81 trytes) which can be used to validate the integrity and validity of the address.
An address with checksum is 90 trytes long, 81 trytes for the address itself and 9 trytes for the checksum.
The procedure to calculate an address checksum is as follows:
Start with an IOTA address (81 trytes).Address (trytes): FSAFM ... NVDZC
Convert the address (81 trytes) to trits (= 81 x 3 = 243 trits)
Address (trits): 1,0,-1,1,0,-1 ... -1,0,0,0,1,0
The address is hashed using the Keccak-384 hash algorithm.
Convert the address checksum (243 trits) to trytes (81 trytes): ...PJFNYWVUGKPRTRV
Get the last 9 trytes: VUGKPRTRV
Append the last 9 trytes to the original address: FSAFM ... NVDZCVUGKPRTRV
The address including checksum has a length of 81 + 9 = 90 trytes.
The IOTA light wallet:
Always creates addresses including the checksum.
The addresses are always 90 trytes long.
Always requires receive addresses, with valid checksums when making a transaction.
The receive addresses must be 90 trytes long.
Check out all my other IOTA tutorial videos:
https://goo.gl/aNHf1y
Subscribe to my YouTube channel:
https://goo.gl/61NFzK
The presentation used in this video tutorial can be found at:
https://www.mobilefish.com/developer/iota/iota_quickguide_tutorial.html
#mobilefish #howto #iota

Views: 2475
Mobilefish.com

Sparse Permutations with Low Differential Uniformity

Views: 81
Institut Fourier

Views: 292
Quantum Information and Computing

Adam Becker, PhD is an astrophysicist and science writer. His new book What Is Real? explores the history of quantum foundations and the questions that remain to be answered.
Get the book: https://goo.gl/s2NGWM

Views: 6117
Talks at Google

Amplifying Privacy in Privacy Amplification by Leonid Reyzin, Yevgeniy Dodis, Divesh Aggarwal, Eric Miles, Zahra Jafargholi. Talk at Crypto 2014.

Views: 282
TheIACR

A quantum computer is a computation device that makes direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from digital computers based on transistors. Whereas digital computers require data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses qubits (quantum bits), which can be in superpositions of states. A theoretical model is the quantum Turing machine, also known as the universal quantum computer. Quantum computers share theoretical similarities with non-deterministic and probabilistic computers; one example is the ability to be in more than one state simultaneously. The field of quantum computing was first introduced by Yuri Manin in 1980 and Richard Feynman in 1982. A quantum computer with spins as quantum bits was also formulated for use as a quantum space--time in 1969.
As of 2014 quantum computing is still in its infancy but experiments have been carried out in which quantum computational operations were executed on a very small number of qubits. Both practical and theoretical research continues, and many national governments and military funding agencies support quantum computing research to develop quantum computers for both civilian and national security purposes, such as cryptanalysis.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video

Views: 272
Audiopedia

Professor Claude Crépeau of McGill University presents the fourth lecture focused on Integers based cryptography -- specifically lattices. This lecture was part of a series of four lectures during Spring 2013.
Find out more about IQC!
Website - https://uwaterloo.ca/institute-for-quantum-computing/
Facebook - https://www.facebook.com/QuantumIQC
Twitter - https://twitter.com/QuantumIQC

Views: 284
Institute for Quantum Computing

IQC visitor and UCSB researcher Austin Fowler describes the current state of knowledge on how to build a practical quantum computer.
Find out more about IQC!
Website - https://uwaterloo.ca/institute-for-quantum-computing/
Facebook - https://www.facebook.com/QuantumIQC
Twitter - https://twitter.com/QuantumIQC

Views: 7323
Institute for Quantum Computing

Amnon Ta-Shma, Tel Aviv University
https://simons.berkeley.edu/talks/amnon-ta-shma-2017-03-07
Proving and Using Pseudorandomness

Views: 362
Simons Institute

Quantum computing holds the promise to enormously increase computing performance in areas including cryptography, optimization, search, quantum chemistry, materials science, artificial intelligence, machine learning, personalized medicine and drug discovery. Quantum computing hardware is maturing swiftly. Depending on the expert you talk with, quantum computing is around the corner or a few years away. Concurrently, research on algorithms that take advantage of quantum computing is also moving briskly. In this discussion, panelists will look at where we are in both theory and practice, where we are headed, and what quantum skills the average computer scientist will eventually need.
Moderator: Umesh Vazirani, University of California, Berkeley
Panelists: Dorit Aharonov, Hebrew University of Jerusalem
Jay M. Gambetta, IBM Research
John Martinis, Google and University of California, Santa Barbara
Andrew Chi-Chih Yao (2000 Turing Laureate), Tsinghua University

Views: 2582
Association for Computing Machinery (ACM)

Fix Dependency Error Kodi-The dependency on script.module.urlresolver version-kodi dependency errors-failed to install dependency script.module.urlresolver-dependency error kodi.
******************************************************************
I get the following error message/notification while try to install the exodus on kodi 17.3 krypton:
Exodus
The dependency on script.module.urlresolver version
or
Failed to install dependency script.module.liveresolver
******************************************************************
This tutorial is about how to fix failed to install dependency exodus.
This error "script.exodus.artwork" solution is works on kodi all versions like that kodi 17,kodi 17.1,kodi 16,kodi 16.1,kodi firestick,xbmc kodi also.
This kodi open source media software is also available for android users,you can get it from google play store.
******************************************************************
Fix failed to install dependency kodi:
1.Goto your kodi home then goto settings, by click to settings icon and goto "File manager".
2.Here you can click to open "Add source" option and you can enter the following i mentioned url.
3.Now you can goto kodi home -addons, here you can click to open "Box icon" and goto "Install from zip file".
4.Here you can locate "Caz" and click to open it,now goto "Repository" then select "repository.simplycaz.zip" file.
5.Now wait for sometime and then goto "Install from repository" - simply caz repo - video addons.
6.Finally you can locate "Exodus" and click to install it.
7.Now the problem "kodi dependency issue" is solved.
8.Using this way also you can fix "kodi dependency script.module.metahandler" error.
******************************************************************

Views: 54481
Teconz

© 2018 Articles about social concerns

With the above announcement by Bitcoin Superstore via their twitter handle, users can almost in an instant complete settlements with XRP while purchasing from different retail outlets. These outlets being the leading ones like eBay, Amazon and others. If you choose to go for this option remember that XRP in the past has given out results of being cheap for both the merchant offering to accept the token and the user. Or, even shorter, build a massive, level playing field in which assets can compete to bridge payments, then try to make XRP a winner on that playing field. This is an ambitious, maybe even crazy, plan. But Ripple has raised tens of millions of dollars, has over a hundred full time employees, and our successes to date speak for themselves. That is, of course, no guarantee of success.