“Anything big happening?” he asked of the quantum information theorist.Syndicated copies to:
To be published by Cambridge University Press in April 2018.
Upon publication this book will be available for purchase through Cambridge University Press and other standard distribution channels. Please see the publisher's web page to pre-order the book or to obtain further details on its publication date.
A draft, pre-publication copy of the book can be found below. This draft copy is made available for personal use only and must not be sold or redistributed.
This largely self-contained book on the theory of quantum information focuses on precise mathematical formulations and proofs of fundamental facts that form the foundation of the subject. It is intended for graduate students and researchers in mathematics, computer science, and theoretical physics seeking to develop a thorough understanding of key results, proof techniques, and methodologies that are relevant to a wide range of research topics within the theory of quantum information and computation. The book is accessible to readers with an understanding of basic mathematics, including linear algebra, mathematical analysis, and probability theory. An introductory chapter summarizes these necessary mathematical prerequisites, and starting from this foundation, the book includes clear and complete proofs of all results it presents. Each subsequent chapter includes challenging exercises intended to help readers to develop their own skills for discovering proofs concerning the theory of quantum information.
h/t to @michael_nielsen via Nuzzel
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John Watrous's excellent quantum book just came out. It's still available free on his webpage: https://t.co/D2rr5FTly6
— michael_nielsen (@michael_nielsen) April 28, 2018
Co-Founder and CEO at Cambridge Quantum Computing
Dear god, I wish Ilyas had a traditional blog with a true feed, but I’m willing to put up with the inconvenience of manually looking him up from time to time to see what he’s writing about quantum mechanics, quantum computing, category theory, and other areas of math.
The books introduce subjects like rocket science, quantum physics and general relativity — with bright colors, simple shapes and thick board pages perfect for teething toddlers. The books make up the Baby University series — and each one begins with the same sentence and picture — This is a ball — and then expands on the titular concept.
Ooh! We definitely need more books like these in early childhood education.Syndicated copies to:
We discuss properties of the "beamsplitter addition" operation, which provides a non-standard scaled convolution of random variables supported on the non-negative integers. We give a simple expression for the action of beamsplitter addition using generating functions. We use this to give a self-contained and purely classical proof of a heat equation and de Bruijn identity, satisfied when one of the variables is geometric.
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Just over a year ago a senior Google engineer (Greg Corrado) explained why quantum computers, in the opinion of his research team did not lend themselves to Deep Learning techniques such as convolutional neural networks or even recurrent neural networks.
As a matter of fact, Corrado’s comments were specifically based on Google’s experience with the D-Wave machine, but as happens so often in the fast evolving Quantum Computing industry, the nuance that the then architecture and capacity of D-Wave’s quantum annealing methodology did not (and still does not) lend itself to Deep Learning or Deep Learning Neural Network (“DNN”) techniques was quickly lost in the headline. The most quoted part of Corrado’s comments became a sentence that further reinforced the view that Corrado (and thus Google) were negative about Deep Learning and Quantum Computing per-se and quickly became conflated to be true of all quantum machines and not just D-Wave :
“The number of parameters a quantum computer can hold, and the number of operations it can hold, are very small” (full article here).
The headline for the article that contained the above quote was “Quantum Computers aren’t perfect for Deep Learning“, that simply serves to highlight the less than accurate inference, and I have now lost count of the number of times that someone has misquoted Corrado or attributed his quote to Google’s subsidiary Deep Mind, as another way of pointing out limitations in quantum computing when it comes either to Machine Learning (“ML”) more broadly or Deep Learning more specifically.
Ironically, just a few months earlier than Corrado’s talk, a paper written by a trio of Microsoft researchers led by the formidable Nathan Wiebe (the paper was co-authored by his colleagues Ashish Kapoor and Krysta Svore) that represented a major dive into quantum algorithms for deep learning that would be advantageous over classical deep learning algorithms was quietly published on arXiv. The paper got a great deal less publicity than Corrado’s comments, and in fact even as I write this article more than 18 months after the paper’s v2 publication date, it has only been cited a handful of times (copy of most recent updated paper here)
Before we move on, let me deal with one obvious inconsistency between Corrado’s comments and the Wiebe/Kapoor/Svore (“WKS”) paper and acknowledge that we are not comparing “apples with apples”. Corrado was speaking specifically about the actual application of Deep Learning in the context of a real machine – the D-Wave machine, whilst WKS are theoretical quantum information scientists and their “efficient” algorithms need a machine before they can be applied. However, that is also my main point in the article. Corrado was speaking only about D-Wave, and Corrado is in fact a member of the Quantum Artificial Intelligence team, so it would be a major contradiction if Corrado (or Google more broadly) felt that Quantum Computing and AI were incompatible !
I am not here speaking only about the semantics of the name of Corrado’s team. The current home page, as of Nov 27th 2016, for Google’s Quantum AI Unit (based out in Venice Beach, LA) has the following statement (link to the full page here):
“Quantum Computing merges two great scientific revolutions of the 20th century: computer science and quantum physics. Quantum physics is the theoretical basis of the transistor, the laser, and other technologies which enabled the computing revolution. But on the algorithmic level today’s computing machinery still operates on “classical” Boolean logic. Quantum computing is the design of hardware and software that replaces Boolean logic by quantum law at the algorithmic level. For certain computations such as optimization, sampling, search or quantum simulation this promises dramatic speedups. Soon we hope to falsify the strong Church-Turing thesis: we will perform computations which current computers cannot replicate. We are particularly interested in applying quantum computing to artificial intelligence and machine learning. This is because many tasks in these areas rely on solving hard optimization problems or performing efficient sampling”
There is a lot to digest in that quote – including the tantalising statement about the strong “Church-Turing Thesis” (“CTT”). Coincidentally this is a very rich area of debate and research that if even trivially followed in this article would take up far more space than is available. For those interested in the foundational aspects of CTT you could do worse than invest a little time listening to the incomparable Scott Aaronson who spoke over summer on this topic (link here). And just a last word on CTT whilst we are on the subject, few, if anyone, will speculate right now that quantum computers will actually threaten the original Church-Turing Thesis and in the talk referenced above, Scott does a great job in outlining just why that is the case. Ironically the title of his talk is “Quantum Supremacy” and the quote that I have taken from Google’s website is directly taken from the team led by Hartmut Neven who has stated very publicly that Google will achieve that standard (ie Quantum Supremacy) in 2017.
Coming back to Artificial Intelligence and quantum computing, we should remember that even as recently as 14 to 18 months ago, most people would have been cautious about forecasting the advent of even small scale quantum computing. It is easy to forget, especially in the heady days since mid 2016, but none of Google, IBM or Microsoft had unveiled their advances, and as I wrote last week (here), things have clearly moved on very significantly in a relatively short space of time. Not only do we have an open “arms” race between the West and China to build a large scale quantum machine, but we have a serious clash of some of the most important technology innovators in recent times. Amazingly, scattered in the mix are a small handful of start-ups who are also building machines. Above all however, the main takeaway from all this activity from my point of view is that I don’t think it should be surprising that converting “black-box”neural network outputs into probability distributions will become the focus for anyone approaching DNN from a quantum physics and quantum computing background.
It is this significant advance that means that for the very same reason that Google/IBM/Microsoft talk openly about their plans to build a machine (and in the case of Google an acknowledgement that they have actually now built a quantum computer of their own) means that one of the earliest applications likely to be tested on even proto-type quantum computers will be some aspect of Machine Learning. Corrado was right to confirm that in the opinion of the Google team working at the time, the D-Wave machine was not usable for AI or ML purposes. It was not his fault that his comments were mis-reported. It is worth noting that one of the people most credibly seen as the “grandfather” of AI and Machine Learning, Geoffrey Hinton is part of the same team at Google that has adopted the Quantum Supremacy objective. There are clearly amazing teams assembled elsewhere, but where quantum computing meets Artificial Intelligence, then its hard to beat the sheer intellectual fire power of Google’s AI team.
Outside of Google, a nice and fairly simple way of seeing how the immediate boundary between the theory of quantum machine learning and its application on “real” machines has been eroded can be seen by looking at two versions of exactly the same talk by one of the sector’s early cheer leaders, Seth Lloyd. Here is a link to a talk that Lloyd gave through Google Tech Talks in early 2014, and here is a link to exactly the same talk except that it was delivered a couple of months ago. Not surprisingly Lloyd, as a theorist, brings a similar approach to the subject as WKS, but in the second of the two presentations, he also discusses one of his more recent pre-occupations in analysing large data sets using algebraic topological methods that can be manipulated by a quantum computer.
For those of you who might not be familiar with Lloyd I have included a link below to the most recent form of his talk on a quantum algorithm for large data sets represented by topological analysis.
One of the most interesting aspects that is illuminated by Lloyds position on quantum speed up using quantum algorithms for classical machine learning operations is his use of the example of the “Principal Component Analysis” algorithm (“PCA”). PCA is one of the most common machine learning techniques in classical computing, and Lloyd (and others) have been studying quantum computing versions for at least the past 3 to 4 years.
Finding a use case for a working quantum algorithm that can be implemented in a real use case such as one of the literally hundreds of applications for PCA is likely to be one of the earliest ways that quantum computers with even a limited number of qubits could be employed. Lloyd has already shown how a quantum algorithm can be proven to exhibit “speed up” when looking just at the number of steps taken in classifying the problem. I personally do not doubt that a suitable protocol will emerge as soon as people start applying themselves to a genuine quantum processor.
At Cambridge Quantum Computing, my colleagues in the quantum algorithm team have been working on the subject from a different perspective in both ML and DNN. The most immediate application using existing classical hardware has been from the guys that created ARROW> , where they have looked to build gradually from traditional ML through to DNN techniques for detecting and then classifying anomalies in “pure” times series (initially represented by stock prices). In the recent few weeks we have started advancing from ML to DNN, but the exciting thing is that the team has always looked at ARROW> in a way that lends itself to being potentially upgraded with possible quantum components that in turn can be run on early release smaller scale quantum processor. Using a team of quantum physicists to approach AI problems so they can ultimately be worked off a quantum computer clearly has some advantages.
There are, of course, a great many areas other than the seemingly trivial sphere of finding anomalies in share prices where AI will be applied. In my opinion the best recently published overview of the whole AI space (an incorporating the phase transition to quantum computing) is the Fortune Article (here) that appeared at the end of September and not surprisingly the focus on medical and genome related AI applications for “big” data driven deep learning applications figure highly in that part of the article that focuses on the current state of affairs.
I do not know exactly how far we are away from the first headlines about quantum processors being used to help generate efficiency in at least some aspects of DNN. My personal guess is that deep learning dropout protocols that help mitigate the over-fitting problem will be the first area where quantum computing “upgrades” are employed and I suspect very strongly that any machine that is being put through its paces at IBM or Google or Microsoft is already being designed with this sort of application in mind. Regardless of whether we are years away or months away from that first headline, the center of gravity in AI will have moved because of Quantum Computing.
It is argued that if the non-unitary measurement transition, as codified by Von Neumann, is a real physical process, then the "probability assumption" needed to derive the Second Law of Thermodynamics naturally enters at that point. The existence of a real, indeterministic physical process underlying the measurement transition would therefore provide an ontological basis for Boltzmann's Stosszahlansatz and thereby explain the unidirectional increase of entropy against a backdrop of otherwise time-reversible laws. It is noted that the Transactional Interpretation (TI) of quantum mechanics provides such a physical account of the non-unitary measurement transition, and TI is brought to bear in finding a physically complete, non-ad hoc grounding for the Second Law.
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. 
Peter Woit has just made the final draft (dated 10/25/16) of his new textbook Quantum Theory, Groups and Representations: An Introduction freely available for download from his website. It covers quantum theory with a heavy emphasis on groups and representation theory and
“contains significant amounts of material not well-explained elsewhere.” He expects to finish up the diagrams and publish it next year some time, potentially through Springer.
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Learn about quantum computation and quantum information in this advanced graduate level course from MIT.
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About this course
Already know something about quantum mechanics, quantum bits and quantum logic gates, but want to design new quantum algorithms, and explore multi-party quantum protocols? This is the course for you!
In this advanced graduate physics course on quantum computation and quantum information, we will cover:
- The formalism of quantum errors (density matrices, operator sum representations)
- Quantum error correction codes (stabilizers, graph states)
- Fault-tolerant quantum computation (normalizers, Clifford group operations, the Gottesman-Knill Theorem)
- Models of quantum computation (teleportation, cluster, measurement-based)
- Quantum Fourier transform-based algorithms (factoring, simulation)
- Quantum communication (noiseless and noisy coding)
- Quantum protocols (games, communication complexity)
Research problem ideas are presented along the journey.
What you’ll learn
- Formalisms for describing errors in quantum states and systems
- Quantum error correction theory
- Fault-tolerant quantum procedure constructions
- Models of quantum computation beyond gates
- Structures of exponentially-fast quantum algorithms
- Multi-party quantum communication protocols
Meet the instructor
Isaac Chuang Professor of Electrical Engineering and Computer Science, and Professor of Physics MIT
Went on vacation or fell asleep at the internet wheel this week? Here’s some of the interesting stuff you missed.
Science & Math
- Context Specific and Differential Gene Co-expression Networks via Bayesian Biclustering | PLOS Computational Biology
- The Competing Incentives of Academic Research in Mathematics
- [1607.08473] Quantum circuits and low-degree polynomials over F_2
- This Physics Pioneer Walked Away from it All | Nautilus
- Monumental proof to torment mathematicians for years to come: Conference on Shinichi Mochizuki’s work inspires cautious optimism. | Nature
- What Your Brain Looks Like When It Solves a Math Problem | New York Times
- Habits of Highly Mathematical People
- Why You Should Care About High-Dimensional Sphere Packing | Roots of Unity
- Initial steps toward reproducible research
- Bridging the Curation Gap between Research and Libraries – A Case Study
- Quantum steampunk: Quantum information applied to thermodynamics
- How Vector Space Mathematics Reveals the Hidden Sexism in Language
- How Sound Can Make Food Taste Better | Nautilus
- Top 10 algorithms of 20th century numerical analysis, from a talk by Alex Townsend
- UK vs. US: Who’s got the right way to teach math(s)? | Math with Bad Drawin
- Physics & Caffeine: Stop Motion Film Uses a Cup of Coffee to Explain Key Co
- The Water Kingdom: A Secret History of China by Philip Ball (review)
- The master of them all: Book review for”Leonhard Euler: Mathematical Genius in the Enlightenment” | The Economist
- Biologists Search for New Model Organisms: The bulk of biological research is centered on a handful of species. Are we missing a huge chunk of life’s secrets?
- One-sentence proof of Fermat’s theorem on sums of two squares | Fermat’s Library
- This protein designer aims to revolutionize medicines and materials
- Our last common ancestor inhaled hydrogen from underwater volcanoes
- Meet Luca, The Ancestor of All Living Things | New York Times
- *Disconnected, fragmented, or united? a trans-disciplinary review of network
- What’s Behind A Science vs. Philosophy Fight? | Big Think
- What is a “Neutral Network” Anyway? An Exploration and Rediscovery of the Aims of Net Neutrality in Theory and Practice
- The Brachistochrone Curve: The Problem of Quickest Descent | Fermat’s Library
- In what sense is Quantum Mechanics a theory of information? | Quora
- Major transitions in information technology | Philosophical Transactions of
- Human brain mapped in unprecedented detail: Nearly 100 previously unidentified brain areas revealed by examination of the cerebral cortex. | Nature
- Cell biologists should specialize, not hybridize: Dry cell biologists, who bridge computer science and cell biology, should have a pivotal role in driving effective team science, says Assaf Zaritsky | Nature
- Internet 3.0: How we take back control from the giants | New Scientist
- How a Guy From a Montana Trailer Park Overturned 150 Years of Biology | The Atlantic
- People can sense single photons | Nature News & Comment
- Defining synergy thermodynamically using quantitative measurements of entropy and free energy
- A Prime Case of Chaos | AMS.org
- Murray Gell-Mann (video interviews) – YouTube
- Mathematics & Chalk: A teary goodbye to Hagomoro | Jeremy Kun
- Want to Change Academic Publishing? Just Say No | Chronicle
- Textbooks Show Aging Signs: Curated Guides Are Next – 10+ Disruptive Factors Transforming the World of Education and Learning — Consequences, Opportunities, Tools
- Simon & Schuster, Penguin, Random House Don’t Want to Talk About Their Ebook Sales
- Amazon Sales Rank: Taming the Algorithm | Self-Publishing Author Advice
- What Authors Should Know About Advance Review Copies
- Ingram Launches Ingram Academic Services
- How a Publishing House Designs a Book Cover
- How Indie Bookstores Help Drive Book Discoverability
- How to Grow Your Email List
- 3 Ways Indie Publishers Sell Books | Digital Book World
- 10 Self-Publishing Trends to Watch
- Ingram Launches Academic Services for University Presses and Academic Publishers
- Indigo Goes Where Amazon, B&N, Goodreads, and a Dozen Publishers and Startus Have Dared to Tread
- How To Make An Ebook Feel More Like A Real Book
- Looking for open digital collections – Wynken de Worde
Indieweb, Internet, Identity, Blogging, Social Media
- What is Open Source?
- My Text Editor is Absolutely Sublime | Devon Zuegel
- My zsh aliases | Devon Zuegel
- XOXO Festival
- Web Design in 4 minutes
- Custom Elements
- Design Principles
- Infographic: The Optimal Length for Every Social Media Update
- Notes For New (and Potential) Twitter Followers | Whatever
- How Blogs Work Today – Whatever
- My reply to: How Blogs Work Today | Whatever
- Unicode Character ‘ZERO WIDTH SPACE’ (U 200B)
- A Book Apart, Practical SVG
- Gillmor Gang Trumpathon
- The best news aggregation service – The Sweet Setup
- Social Startup Sprinklr Is Now Valued At $1.8 Billion After $105 Million Raise | Forbes
- Epeus’ epigone: Digital publics, Conversations and Twitter
- The New Meaning of Success
- 7 Lessons from the Future of Content: Part One — Tools Are Cheap, Time Is Expensive
- 7 Lessons from the Future of Content: Part Two — Let’s Play Risk
- Aron Pilhofer Joining Temple University School of Media and Communication
- Secrets and agents: George Akerlof’s 1970 paper, “The Market for Lemons”, is a foundation stone of information economics. The first in our series on seminal economic ideas | The Economist
- John Oliver has the takedown of Donald Trump’s Republican convention
- Reference: New Interactive Map Of 100,000 Photos and Videos Reveal “Lost London in the Victorian Era”
- “better modifiers than “insane(ly)” (Grammar and Usage)
- A lesson in the errors of statistical thinking: Nate Silver on Trump
- Trump & Putin. Yes, It’s Really a Thing
- Charlie Parker Plays with Dizzy Gillespie in Only Footage Capturing the “Bird” in True Live Performance
- Let Me Remind You Fuckers Who I Am (Shit HRC Can’t Say/satire)
I’m already a major chunk of the way through the book, having had an early ebook version of the text prior to publication. This is the published first edition with all the diagrams which I wanted to have prior to finishing my full review, which is forthcoming.
One thing I will mention is that it’s got quite a bit more philosophy in it than most popular science books with such a physics bent. Those who aren’t already up to speed on the math and science of modern physics can certainly benefit from the book (like most popular science books of its stripe, it doesn’t have any equations — hairy or otherwise), and it’s certain to help many toward becoming members of both of C.P. Snow’s two cultures. It might not be the best place for mathematicians and physicists to start moving toward the humanities with the included philosophy as the philosophy is very light and spotty in places and the explanations of the portions they’re already aware of may put them out a bit.
I’m most interested to see how he views complexity and thinking in the final portion of the text.
More detail to come…Syndicated copies to:
Running a brain-twisting thought experiment for real shows that information is a physical thing – so can we now harness the most elusive entity in the cosmos?
This is a nice little overview article of some of the history of thermodynamics relating to information in physics and includes some recent physics advances as well. There are a few references to applications in biology at the micro level as well.
- Second Law of Thermodynamics with Discrete Quantum Feedback Control by Takahiro Sagawa and Masahito Ueda; Phys. Rev. Lett. 100, 080403 – Published 26 February 2008
- Work and information processing in a solvable model of Maxwell’s demon by Dibyendu Mandal and Christopher Jarzynski; PNAS vol. 109 no. 29, July 17, 2012
- Thermodynamic Costs of Information Processing in Sensory Adaptation by Pablo Sartori, Léo Granger, Chiu Fan Lee, and Jordan M. Horowitz; PLOS December 11, 2014 http://dx.doi.org/10.1371/journal.pcbi.1003974
- Intermittent transcription dynamics for the rapid production of long transcripts of high fidelity by Depken M1, Parrondo JM, Grill SW; Cell Rep. 2013 Oct 31;5(2):521-30. doi: 10.1016/j.celrep.2013.09.007
- The stepping motor protein as a feedback control ratchet by Martin Bier; BioSystems 88 (2007) 301–307
In catching up on blogs/reading from the holidays, I’ve noticed that physicist Sean Carroll has a forthcoming book entitled The Big Picture: On the Origins of Life, Meaning, and the Universe Itself (Dutton, May 10, 2016) that will be of interest to many of our readers. One can already pre-order the book via Amazon.
Prior to the holidays Sean wrote a blogpost that contains a full overview table of contents, which will give everyone a stronger idea of its contents. For convenience I’ll excerpt it below.
I’ll post a review as soon as a copy arrives, but it looks like a strong new entry in the category of popular science books on information theory, biology and complexity as well as potentially the areas of evolution, the origin of life, and physics in general.
As a side bonus, for those reading this today (1/15/16), I’ll note that Carroll’s 12 part lecture series from The Great Courses The Higgs Boson and Beyond (The Learning Company, February 2015) is 80% off.
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THE BIG PICTURE: ON THE ORIGINS OF LIFE, MEANING, AND THE UNIVERSE ITSELF
* Part One: Cosmos
- 1. The Fundamental Nature of Reality
- 2. Poetic Naturalism
- 3. The World Moves By Itself
- 4. What Determines What Will Happen Next?
- 5. Reasons Why
- 6. Our Universe
- 7. Time’s Arrow
- 8. Memories and Causes
* Part Two: Understanding
- 9. Learning About the World
- 10. Updating Our Knowledge
- 11. Is It Okay to Doubt Everything?
- 12. Reality Emerges
- 13. What Exists, and What Is Illusion?
- 14. Planets of Belief
- 15. Accepting Uncertainty
- 16. What Can We Know About the Universe Without Looking at It?
- 17. Who Am I?
- 18. Abducting God
* Part Three: Essence
- 19. How Much We Know
- 20. The Quantum Realm
- 21. Interpreting Quantum Mechanics
- 22. The Core Theory
- 23. The Stuff of Which We Are Made
- 24. The Effective Theory of the Everyday World
- 25. Why Does the Universe Exist?
- 26. Body and Soul
- 27. Death Is the End
* Part Four: Complexity
- 28. The Universe in a Cup of Coffee
- 29. Light and Life
- 30. Funneling Energy
- 31. Spontaneous Organization
- 32. The Origin and Purpose of Life
- 33. Evolution’s Bootstraps
- 34. Searching Through the Landscape
- 35. Emergent Purpose
- 36. Are We the Point?
* Part Five: Thinking
- 37. Crawling Into Consciousness
- 38. The Babbling Brain
- 39. What Thinks?
- 40. The Hard Problem
- 41. Zombies and Stories
- 42. Are Photons Conscious?
- 43. What Acts on What?
- 44. Freedom to Choose
* Part Six: Caring
- 45. Three Billion Heartbeats
- 46. What Is and What Ought to Be
- 47. Rules and Consequences
- 48. Constructing Goodness
- 49. Listening to the World
- 50. Existential Therapy
- Appendix: The Equation Underlying You and Me
- Further Reading