The concepts of identical particles and indistinguishability are fundamental to quantum mechanics, and, therefore, also to quantum computing. I find group theory has helped me to understand identical particles much better.
March 26, 2015
A question I am often asked is what is the difference between tensor networks and quantum Bayesian networks, and is there any advantage to using one over the other.
When dealing with probabilities, I prefer quantum Bayesian networks because b nets are a more natural way of expressing probabilities (and probability amplitudes) whereas tensor nets can be used to denote many physical quantities other than probabilities so they are not tailor made for the job as b nets are. Let me explain in more detail for the technically inclined.
March 24, 2015
Steve Wozniak, co-founder of Apple, is a brilliant, passionate engineer, and a really nice guy too. The guy loves dogs and teaches high school science courses– more than enough reasons for me to like him.
In a recent interview, Woz discussed his feelings and expectations about AI and quantum computers. Check out this news item about what he said:
Apple co-founder Steve Wozniak on robot overlords and electric cars (24 March 2015, by Paul Smith)
“Computers are going to take over from humans, no question,” Mr Wozniak said.
He said he had long dismissed the ideas of writers like Raymond Kurzweil, who have warned that rapid increases in technology will mean machine intelligence will outstrip human understanding or capability within the next 30 years. However Mr Wozniak said he had come to recognize that the predictions were coming true, and that computing that perfectly mimicked or attained human consciousness would become a dangerous reality.
Mr Wozniak said the negative outcome could be stopped from occurring by the likely end of Moore’s Law, the pattern whereby computer processing speeds double every two years.
So unless scientists can start controlling things at sub-atomic level, by developing so-called quantum computers, humanity will be protected from perpetual increases in computing power.
“For all the time they’ve been working on quantum computing they really have nothing to show that’s really usable for the things we need … researchers can make predictions, but they haven’t been able to get past three qubits yet,” Mr Wozniak said.
“I hope it does come, and we should pursue it because it is about scientific exploring,” Mr Wozniak said. “But in the end we just may have created the species that is above us.”
Okay, it’s not like I’m ever going to meet Woz, but here is what I would say to him if I did.
(Gate model) quantum computers will be built in the next ten years. There is no doubt about that in my mind or in the mind of the vast majority of scientists. There has been much more progress in quantum computing than you realize. And, more importantly, no major hurdles (that violate known physical principles) have been encountered yet, and we are almost there.
Woz, you say you are afraid of what quantum computers can do for AI, but you want this endeavor to succeed because “it’s about scientific exploring”. Then I would advice you to follow the corny dictum, if you can’t beat them, join them. Get directly involved in quantum computing, perhaps by joining the board of directors of a QC company. No better way to make quantum computing move in the right direction than by becoming one of its steersmen.
One more thing…
Quantum computers will teach quantum mechanics to young kids, just like ham radio has taught them electronics and PCs has taught them programming. You Woz, who are so interested in k12 education, should keep this in mind.
March 16, 2015
Geoffrey Hinton, a respected Computer Science/AI Prof at the University of Toronto, has been the subject of many popular sci-tech articles, especially after Google bought his startup DNNresearch Inc. in 2012. (DNN= Deep Neural Networks). I would like to point out that nowadays what is called Deep Learning Neural Nets is really a hybrid of what I call in this blog Bayesian Networks and what was referred to as artificial Neural Nets by Minsky in the 1970’s (although he was by no means the originator of the subject of artificial NNs. The Wikipedia article on artificial neural networks traces back their history as early as 1943, and that leaves out the ancient Greece philosophers, who no doubt said something about them).
You can see the deep integration between Neural and Bayesian networks in Hinton’s work if you look at the slides of the following introductory talk he gave at UCLA in 2012 (he calls them Belief networks instead of Bayesian networks but it’s the same thing). Of course, quantum computers have the potential to do Bayesian Networks and AI calculations much faster than classical computers.
Graduate Summer School: Deep Learning, Feature Learning,
July 9 – 27, 2012, IPAM/UCLA
Geoffrey Hinton (University of Toronto)
PART 1: Introduction to Deep Learning & Deep Belief Nets (PDF Parts 1 & 2)
PART 2: Using backpropagation for fine-tuning a generative model to be better at discrimination
(My thanks to jesuslopez for alerting me to this link)
March 15, 2015
A Bayesian network is a DAG (directed acyclic graph) for which each of its nodes is assigned a transition matrix. Say a node has 2 incoming arrows , , and an outgoing arrow . Then one assigns to that node a transition matrix/conditional probability , where . But what happens if are all equal to a group ? Then one can define group multiplication as a B net node. Then one can translate any group theory statement to a statement about B nets. This means that there is some justification in saying that the vast collection of facts that we call Group Theory can all be viewed as a subset of the discipline of Bayesian Networks. Wow!
I’ve prepared a 3 page appendix to this blog post which you can find here:
In the appendix, I give a more detailed and formal explanation of how one can define some elementary group theory concepts (for instance, invariant groups, cosets, coset multiplication) in terms of B nets.
I like to think of B nets as being a very BROAD CANVAS, and this observation that Group theory is a mere subset of B nets, sets my heart aflutter :)
Of course, there is always someone bigger. B nets are themselves a subset (but a powerful and physicist-friendly one) of category theory (I know nothing about category theory, with my apologies to my friends who do).
P.S. After my religious conversion/epiphany, I continue to learn more and more about group theory. I feel my GT superpowers increasing day by day. I am becoming a lean, mean, group theory thinking machine. My GT thinking is beginning to float like a butterfly and sting like a bee. My inspiration is the greatest, wisest boxer of all time, Muhammad Ali.
Of course, the conventional notation for group theory is more than adequate, and very efficient, so expressing the same concepts in a less succinct language based on B nets may seem to some as a step backwards instead of forwards. But that is not the point of this blog post. The point is to show that group theory can be expressed in terms of B nets.
I should mention that using DAGS to describe group theory operations is a well known idea. The purpose of this post is not to communicate an original idea of mine, but to disseminate an idea that I find really cool. The idea in question concerns B nets and therefore aligns well with the main theme of this blog.
March 10, 2015
Okay, Wimpy the string theorist. Here is the String Theory 101 homework due next Tuesday. Find a quantum computer algorithm or simulation (or prove there is none) that will show a measurable difference, not justifiable with classical gravity, in how it runs on the surface of the Earth (or the “surface” of Jupiter with 2.6 earth surface gravity) and in interplanetary space (floating far away from any massive bodies).
[Kirk]: Spock, we are in grave danger. Our quantum computers malfunctioned when we were in close proximity to the neutron star we were studying.
quantum gravity exception
March 9, 2015
It is often said that Albert Einstein had bad math grades in school. There is some truth to that assertion, but unless one delves into the details of Einstein’s life, one might get the impression that Einstein was the most amazing late bloomer in the history of mankind. Not at all.
To begin with, let me emphasize that Einstein was very appreciated and considered a wunderkind by his teachers during his gymnasium, the equivalent of high school. Throughout gymnasium, he got the highest possible grades in Math and Physics. See this NYT article telling us just that. (Einstein did hate French, but who can blame him for that, when he could talk a far cooler language, Italiano, while in Milano with his lifelong buddy, Michelangelo Besso.)
So where does the the myth of Einstein’s bad grades come from? Is there any truth to it? I think so. Albert’s trouble with bad grades started when he reached university. Albert was not a happy camper in college and grad school. Here are some excerpts from the chapter “A very beautiful day” from the book “Reflections on Relativity” by Kevin Brown, available for free on the internet here. I haven’t read Brown’s book, but I highly recommend that you read this small chapter entitled “A very beautiful day”. It’s a very beautiful chapter. Excerpts:
Despite his love of physics, Einstein did not perform very impressively as an under-graduate in an academic setting, and this continued to be true in graduate school. Hermann Minkowski referred to his one-time pupil as a “lazy dog”. As the biographer Clark wrote, “Einstein became, as far as the professorial staff of the ETH was concerned, one of the awkward scholars who might or might not graduate but who in either case was a great deal of trouble”. Professor Pernet at one point suggested to Einstein that he switch to medicine or law rather than physics, saying “You can do what you like, I only wish to warn you in your own interest”. Clearly Einstein “pushed along with his formal work just as much as he had to, and found his real education elsewhere”. Often he didn’t even attend the lectures, relying on Marcel Grossmann’s notes to cram for exams, making no secret of the fact that he wasn’t interested in what men like Weber had to teach him. His main focus during the four years while enrolled at the ETH was independently studying the works of Kirchhoff, Helmholtz, Hertz, Maxwell, Poincare, etc., flagrantly outside the course of study prescribed by the ETH faculty. Some idea of where his studies were leading him can be gathered from a letter to his fellow student and future wife Mileva Maric written in August of 1899
I returned to the Helmholtz volume and am at present studying again in depth Hertz’s propagation of electric force. The reason for it was that I didn’t understand Helmholtz’s treatise on the principle of least action in electrodynamics. I am more and more convinced that the electrodynamics of moving bodies, as presented today, is not correct, and that it should be possible to present it in a simpler way. The introduction of the term “ether” into the theories of electricity led to the notion of a medium of whose motion one can speak without being able, I believe, to associate a physical meaning with this statement. I think that the electric forces can be directly defined only for empty space…
Einstein later recalled that after graduating in 1900 the “coercion” of being forced to take the final exams “had such a detrimental effect that… I found the consideration of any scientific problem distasteful to me for an entire year”. He achieved an overall mark of 4.91 out of 6, which is rather marginal. Academic positions were found for all members of the graduating class in the physics department of the ETH with the exception of Einstein, who seems to have been written off as virtually unemployable, “a pariah, discounted and little loved”, as he later said.
Toward the end of 1901 Einstein had still found no permanent position. As he wrote to Grossmann in December of that year, “I am sure I would have found a position [by now] were it not for Weber’s intrigues against me”. It was only because Grossmann’s father happened to be good friends with Haller, the chief of the Swiss Patent Office, that Einstein was finally given a job, despite the fact that Haller judged him to be “lacking in technical training”. Einstein wrote gratefully to the Grossmann’s that he “was deeply moved by your devotion and compassion which do not let you forget an old, unlucky friend”, and that he would spare no effort to live up to their recommendation. He had applied for Technical Expert 2nd class, but was given the rank of 3rd class (in June 1902).
As soon as he’d been away from the coercive environment of academia long enough that he could stand once again to think about science, he resumed his self-directed studies, which he pursued during whatever free time a slightly lazy patent examiner can make for himself. His circumstances were fairly unusual for someone working on a doctorate, especially since he’d already been rejected for academic positions by both the ETH and the University of Zurich. He was undeniably regarded by the academic community (and others) as “an awkward, slightly lazy, and certainly intractable young man who thought he knew more than his elders and betters”.
The friendship with Besso may have been, in some ways, the most meaningful of Einstein’s life. Michael and his wife sometimes took care of Einstein’s children, tried to reconcile Einstein with Mileva when their marriage was foundering, and so on. Another of the few close personal ties that Einstein was able to maintain over the years was with Max von Laue, who Einstein believed was the only one of the Berlin physicists who behaved decently during the Nazi era. Following the war, a friend of Einstein’s was preparing to visit Germany and asked if Einstein would like him to convey any messages to his old friends and colleagues. After a moment of thought, Einstein said “Greet Laue for me”. The friend, trying to be helpful, then asked specifically about several other individuals among Einstein’s former associates in his homeland. Einstein thought for another moment, and said “Greet Laue for me”.
Seems like Albert got bad math grades, not in high school but at the uni., and not because he was a lazy dog, but because he felt that his university (ETH Zurich, considered then and now one of the best technical universities in the world) addressed very poorly the needs of its students. (Albert also seems to have felt that many university academics were not very moral people. I’ve experienced that myself in quantum computation many times and documented some of it in this blog).
The bad news for us is that universities change at a glacial pace. They are pretty much the same today as they were in the early 1900 when Einstein attended one.
The good news is that MOOCs are going to change drastically the current university system. For more info about my opinion of MOOCs, follow this link.
Some people might say that Einstein was unique, far above the rest of his class, and that he was a self-studier at heart. How could a university satisfy his needs, and those of every other student as well. Precisely. That’s why a modern teaching system like MOOCs can be taken at different speeds by different students, and students can choose teachers from a large pool of possible candidates from all around the world, leading them to find a teacher that thinks the same way they do. Of course, current university systems do none of this, and they are outrageously overpriced too.
March 5, 2015
Check out this exciting new paper by a bunch of prestigious String Theorists:
“A bound on chaos” by Maldacena, Shenker and Stanford, http://arxiv.org/abs/1503.01409
Lubos Motl has a nice blog post entitled “Taming the Butterfly Effect” about the paper. However, Lubos seems unaware of the fact that quantum information theorists beat string theorists to the punch on this one. Our very own quantum information theorist Seth Lloyd came up with the same concept more than a year ago, except that he called it the “Twitter Rate Upper Bound”. Lloyd has provided an ironclad proof of the existence of such an upper bound for a Turing complete “inflationary quantum computer”. Seth Lloyd has also explained the source of Dark Energy much better than any string theorist ever has.
March 1, 2015
To boldly go where no man has gone before.
Space, the final frontier.
Live long and prosper, Leonard Nimoy.
The TV series Star Trek inspired many baby boomers to dream about space travel, and, sometimes, to pursue careers in science and engineering. By far, one of the main attractions of the series was Dr. Spock or Mr. Spock, chief science officer of the starship Enterprise (played by Leonard Nimoy, who passed away a few days ago. RIP). Dr. Spock epitomizes the voice of pure, flawless logic inside everyone of us. Dr. Spock has achieved the rare distinction of becoming a universally known fictional character, an archetype, and a scientist too. I dare say 99% of the population of the world is familiar with Dr. Spock’s looks and quirky personality. This has been true since the first Star Trek episode aired in 1966, and continues to be true today.
P.S. I am currently writing a paper applying Group Theory to quantum computing. The paper is going very well, but it’s still very far from completion. It’s going to be a long one.
February 26, 2015
Since time immemorial, scientists have been grappling with the thorny, open, research-question of what does a quantum computer look like (or rather, will look like). Here is my artist’s rendition. I’m sure better scientists than I can come up with more elevating and edifying portrayals, but this is my own, dammit. Work with me here. (This picture was inspired by my previous blog post. It is based on this image. I also used pictures of Atlas, a robot made by the Boston Dynamics company, which is now owned by Google, who must intend to use it to build the first army of robotic soldiers. I hope my Greek friend Angelo aka ElAngelExterminador approves of my allusion to sublime Greek culture).