December 1, 2013
November 24, 2013
“The future belongs to Canada”, according to MacLean’s’ Mark Steyn
quote from TV program “The Simpsons”: (said by Grampa Simpson) “Typical Canadian wimpiness. That’s why you have snowballs and we have the H bomb!”
MacLean’s, a famous right-leaning, franco-phobe Canadian magazine, has just come out with a news article containing their “Power List” of the 10 most powerful Canadians. Mike Lazaridis made the list (by a hair, as number 10). MacLean’s article delivers a well written description of Lazaridis’s efforts in the quantum arena. Well written but not very critical. Me being such a nag, let me provide some of the criticism that is lacking from their article. In particular, let me point out some typical Canadian wimpiness aspects of Lazaridis’ quantum computing efforts.
Here is the article:
Excerpts in boldface. My commentary in non-bold
In 2002, Lazaridis launched his project’s experimental phase, the Institute for Quantum Computing (IQC). Spilling across three buildings including the year-old, state-of-the-art 280,000-sq.-foot Quantum Nano Centre, IQC is home to 200 scientists trying to turn theory into working prototypes for a new technology.
When Lazaridis hired a soft-spoken, Quebec-born student of Stephen Hawking’s named Raymond Laflamme to be the director of the Institute for Quantum Computing in 2002, Laflamme had built a five-qubit “computer,” an incredibly finicky tinker toy. Laflamme is up to a dozen qubits now; he hopes to have machines with 50 to 100 qubits in the next five years. To get this far, Lazaridis has paid $200 million of his own money, an amount roughly matched by a series of investments over 13 years by the Ontario and federal governments.
Laflamme’s 12 qubits are NMR qubits. NMR quantum computers were known to be non-scalable since they were first proposed about 17 years ago. For many years, Laflamme has clung doggedly to them and managed to push them as far as they can go. A great waste of time, since NMR QCs are a non-scalable dead end street.
According to Wikipedia, Laflamme’s original training is as a pure theoretical physicist in quantum gravity and cosmology. Leading a team that invents a practical QC will require an experimentalist of the highest caliber, one guy in a million. Most of the time, great experimentalists and great theorists in physics have very little in common: they are a different species, with different upbringings, interests and talents. There have been some exceptions to this rule of thumb, like Enrico Fermi, but they are very rare. Is Laflamme destined to become Canada’s Fermi? Highly unlikely, unless he is a very late bloomer.There are ZERO U.S. Patents (ref:below) that list him as an inventor even though he is 53 years old (ref: Wikipedia). If he were going to show promise in the experimental arena, he would have done so at a much earlier age. Really great experimentalists are already doing jaw dropping experiments while they are still in high school. If you were trying to assemble a winning hockey team, would you want the team’s coach to be a 50 year old, klutzy, book worm who first developed an interest in sports a few days ago?
Laflamme showed me sheets of factory-made diamond with precisely inserted impurities, individual atoms poked into the carbon lattice with microscopic accuracy. The resulting material has quantum properties. He showed me a sensor made of silicon and etched aluminum. An IQC researcher, Adrian Lupascu, had an insight: If quantum states are incredibly delicate and prone to break down, their very fragility can make them useful for sensors. “These are the best magnetometers there are, the size of microns . . . an order of magnitude more sensitive than anything else.” They’ll have applications in medical imaging, manufacturing and microscopy.
In other words, 11 years after they started in 2002, the best they have to show for a 200 million dollar investment (plus 200 matching grant from the government) is a magnetic sensor. They are a million miles away from constructing a quantum computer. They aren’t even focusing on that.
Laflamme has been recruiting world-class scientists at an accelerating pace: materials scientists, engineers, theorists. His biggest catch by far is David Cory, a nuclear engineer the University of Waterloo poached from the Massachusetts Institute of Technology in 2010 with a $10-million federal grant. Nobody in the world is better at understanding the odd language of quantum particles or in spotting their real-world applications. He came to Canada with three 18-wheelers full of lab equipment. That posed the sort of challenge Lazaridis likes to solve.
Unfortunately, David Cory ‘s specialty is mostly NMR. Cory has worked on quantum computing for at least 17 years (I located an NMR QC paper of his from 1996). The types of QC advances that he has made in those 17 years are almost exclusively in NMR, a non-scalable, dead end street for quantum computers from day one. A patent search shows only 1 U.S. patent (ref. below) with him as inventor, not too impressive for a fairly old experimentalist. (I couldn’t find his age on the Internet but I believe he is 50-60 years old).
Cory has an unusually large team of graduate students and post-doctoral assistants from a wide variety of disciplines. The entire team meets every morning. Nobody is allowed to work on individual projects. They have found applications for their work in medical imaging and in deep-sea oil exploration. “We’ve started exploring with the Princess Margaret Cancer Centre” in Toronto, Cory said. “Just an open-ended discussion. How can quantum sensors make a difference? And there’ll be many ways. It’ll build on old work we did at the Dana-Farber cancer centre in Boston, using quantum sensors to set the edges of soft-tissue sarcomas.”
Just what I suspected. Cory wants everyone in his team to follow his vision (which seems to comprise mainly what is familiar to him, i.e., NMR related stuff). They are working almost exclusively on quantum sensors, which is quite different from working to build a QC.
In September, IQC named its two latest recruits. Amir Yacoby comes from Harvard University and is a world leader in developing these exotic materials that can hang onto quantum characteristics. Steve MacLean is an astronaut: he served on the International Space Station in 2006 and was the president of the Canadian Space Agency from 2008-13. But MacLean is also a physicist who was setting up an elaborate experiment in his garage—he won’t discuss details—when he bumped into Lazaridis a few years ago at Cape Canaveral before a space shuttle launch. “We ended up talking for two hours about everything and nothing.” Soon MacLean had offices at Perimeter and at IQC. He also serves on the advisory board of the new venture-capital firm.
According to Wikipedia, Steve MacLean got a Ph.D. in laser physics in 1983 (at the age of 29, fairly late for typical PhDs), but most of his career has been as an administrator, gymnastic athlete, and astronaut.There are ZERO U.S. Patents (ref:below) that list him as an inventor even though he is 58 years old (ref:Wikipedia).
As for Amir Yacoby, he seems to have been an academic most of his life. I found only 3 U.S. Patents (ref. below) listing him as an inventor, again not too impressive for a fairly old experimentalist (I couldn’t find his age on the Internet but he looks from his photos to be 50-60).
Quite frankly, judging from their WIMPY patent record, I do NOT expect either Laflamme, or Cory, or MacLean or Yacoby to be the first scientists to build a practical gate model QC.
What are they doing? MacLean won’t say.
“You know what I’m doing by doing that?” MacLean said in an attempt to explain his silence. “I’m protecting Canada in a way. I mean, this is a community effort that we’re doing here and we have certain leads in certain areas and I just would like you to focus on the fact that it’s unique.”
Only Lazaridis can talk about what goes on at QVI. He doesn’t say much either. But he reveals that the fund has made its first investment. “Actually, we only went public after we did our first investment.”
What’s the investment?
“I can’t tell you that.”
What’s the scale of the investment?
What field is it in? Is it in sensors? Cryptography?
“Those were already announced before we made our investment. Our investment is different.”
Will it lead to products on the market? Yes, Lazaridis said, perhaps in two or three years. Products for consumers? “I can’t really tell you.”
He finally said that the entrepreneur QVI just funded is “a guy from around here” and that when he wrote an equation on a blackboard, “I said, ‘We have to invest in this.’ This is not just an improvement, this is not just a new way of doing a classical thing that we’re all used to. This is something new.”
Well, I think that such excessive coyness from Lazaridis is counterproductive and self-defeating. That is what patents are for, to allow partial disclosure without losing all rights to an invention. Even Google started with a patent. Do Lazaridis’ people have any patents at all to back up all their hot air? Just by saying that they are working on a magnetic sensor or a photonic QC or whatever, (and then pointing to some patents) would not give the store away. It would actually garner free publicity and serve to enlist new investors and scientific talent. If I were an investor, I would be very leery and put-off by such excessive coyness on the part of a startup, because it makes them indistinguishable from scam artists, or deluded dreamers.
Furthermore, I would argue that in their case such coyness is not protecting them from any competitors because they are operating in an essentially competitor free environment—I mean, how many other companies are trying to build a QC? (other than D-Wave, and Lazaridis seems totally uninterested in adiabatic quantum computers like D-Wave’s) Of course, I am assuming that Lazaridis and his coterie mean it when they say that they are trying to build a QC. The truth is they don’t seem to know themselves what they want. They claim that they are determined to build a QC, but they claim this only 3 out every 7 days of the week. Canadian wimps!
patents listing “David Cory” as inventor. Result: 1 patent in quantum physics
- “Compact inhomogeneous permanent magnetic field generator for magnetic resonance imaging” (3 inventors, filed 2009)
patents listing “Amir Yacoby” as inventor. Result: 3 patents in quantum physics:
- “Spin based magnetometer” (7 inventors, filed 2008)
- “Electronic spin based enhancement of magnetometer sensitivity” (7 inventors, filed 2008)
- “Magnetic field sensor device for direct magnetic field imaging and method of fabrication thereof “ (6 inventors, filed 2008)
patents listing “Steve MacLean” as inventor. Result: 0
(also 0 for Stephen MacLean)
- patents listing “Raymond Laflamme” as inventor. Result: 0
November 19, 2013
Lately, I’ve been busy writing 3 papers (for Operation Lisbeth). In the process, I’ve had an “epiphany” experience which I’ve had several times before and which I’d like to describe to you. It’s an experience related to Bayesian networks (B nets). Often, when I have questions of the type: quantum mechanics predicts such and such doesn’t it? Or what does quantum mechanics predict for such and such?, I find that B nets are an excellent “programming language” to answer such questions in a very conclusive and satisfying way, at least for my taste.
Everyone that has ever programmed a computer has had this experience: You start with an algorithm that you think you understand, but after programming it on a computer you end up understanding it much better than before. The process of programming it makes you aware of a lot of subtleties about it that you didn’t realize before.
I find the same is true when I use B nets. I start with a crazy probabilistic algorithm that I think I understand. Then I “program” it in the language of B nets, and all of a sudden I realize how poorly I originally understood it. Often my original algorithm was slightly wrong or incomplete, and the language of B nets comes to the rescue, allowing me to fix the parts that didn’t work at first.
Note that by “programming” my crazy algorithm in the language of B nets, I don’t necessarily mean writing an actual computer program for it. I mean simply stating it in the precise language of B nets. A computer program is not necessary, even though going that extra mile might produce extra satisfaction. Computer software for doing both classical and quantum B nets does already exist, and I believe it will continue to improve in the future. I even believe that quantum computers will revitalize the field of B nets, by allowing us to perform B net calculations much faster, both for classical and quantum B nets.
I have found that this “programming” with B nets strategy works for BOTH classical and quantum mechanical probabilistic algorithms.
For classical algorithms, I program in the language of classical B nets pioneered by Judea Pearl and others. (For an example of this strategy, see for example this paper of mine, in which I review classical Shannon information theory, stated in the language of classical B nets.)
For quantum algorithms, what I like to do is to FIRST find the classical version of the algorithm, and program that in terms of classical B nets. SECOND, I generalize the classical algorithm to quantum mechanics, and program that in the language of quantum B nets (quantum B nets are discussed in this paper). As an example of this TWO STEP STRATEGY, see, for instance, this paper of mine about Maxwell’s Demon.)
Related Blog Posts
November 6, 2013
Secret Message: Operation Lisbeth is going very well
Recently, some press articles have come out claiming that a mod of Minecraft called qCraft, produced by Google, will cause millions of kids to get interested in quantum science and become the quantum scientists of the future. Maybe, or maybe not. Maybe they’ll get hooked on video games and end up as operators of military drone planes.
One of the things that qCraft can “do” is quantum teleportation. This has led some of those future scientist kids to think that the reason Google currently has a barge floating in the San Francisco harbor is that it is planning to teleport it, in broad daylight, into a different universe, using Hartmut Neven’s multiverse theory and D-Wave’s quantum computer. Google has been practicing how to do this with their qCraft quantum simulator. According to qCraft, it should work.
No way kids. D-Wave’s QC is incapable of teleportation, because the degree to which it can entangle things is not sufficient to achieve it. Teleportation can only be achieved by gate model quantum computers, not by adiabatic quantum computers… at least perfect teleportation. At most, adiabatic QCs like D-Wave’s might be able to achieve an imperfect teleportation. Let me illustrate this with an animated gif of the inferior teleportation product sold by Google. If you want perfect teleportation, you can’t have it kid, because Google refuses to work on gate model QCs. Google could invest in both QC types and race them against each other but it hasn’t. Google is no Bell Labs, it’s not even an IBM, it’s more like Ron Popeil‘s Ronco-matics lab.
October 29, 2013
Here is my customary annual Halloween HORROR story. It’s a story about the soon to arrive doomsday for universities as we know them, and about a plague that will soon be unleashed on university professors.
In the Bible, The Book of Revelation speaks of the end days and of the day of judgement. It predicts that a Lamb will open a book with seven seals. Opening the seventh and last seal will unleash seven plagues.
“And when the Lamb had opened the seventh seal, there was silence in heaven about the space of half an hour”.[Rev. 8:1]
A young Physicist knight was slowly making his way back home from the Crusades.
The Crusades had been very disappointing to him. He had gone there with the intention of having fun pillaging, raping and beheading all science infidels who dared to question the wisdom of building a new particle accelerator, the New Jerusalem. The New Jerusalem would be a successor to the LHC, aka the Old Jerusalem, which was by now looking pretty frumpy, after failing to find supersymmetry. The New Jerusalem would be built in Japan. Aligning a machine several kilometers long in Japan, earthquake capital of the world? Priceless. However, the public didn’t agree with the young knight, and wanted to spend their tax money on frivolous things like roads and bridges, and biomedical research. Very disappointing.
What awaited the young Physicist knight at home was even worse than the Crusades…His home town was at that time being racked and decimated by an inexorable, ruthless MOOC-Pox Plague.
At the beginning of the story, a college administrator with a pasty white complexion, dressed in a black hooded robe, tells our knight errant that he is next on the list of profs that will be dismissed to make their university more MOOCish. In a desperate bid to prolong his life, our knight initiates a game of chess with the college administrator, for he realizes that the administrator will not want to fire him until after the chess game is concluded. Deep down, our knight knows full well that he will eventually loose the game to the college administrator, for the administrator is a much better chess player. The college administrator has proven before how adept and ruthless a chess player he is, by granting himself multi-million dollar yearly salaries while paying adjunct professor serfs $300 per course.
The college administrator and our knight continue to play this chess game intermittently as our knight gradually makes his way back to his home town.
At some point, the knight errant witnesses a procession of flagellants (i. e., graduate students and postdocs).
Throughout the story, our young knight keeps wondering why is it that God is so absent and silent in our lives. Oops, then he remembers that he doesn’t believe in God. So that question is pretty silly for him to be asking in this movie.
Near the end, our knight knocks down the pieces of the chess game, pretending to do so unintentionally. He then tells the college administrator that he doesn’t remember where the pieces were. The college administrator replies that he has been recording his every move and the game has been filmed by hidden cameras. He quickly restores the pieces to their former positions and wins on the next move. His last move surprises the audience. It consists of moving a rook labeled Feynman Lectures. We then realize that that rook represents a MOOC, put out by Caltech, based on Feynman’s 3 red books and his video-taped lectures. This MOOC will be a killer app, literally. It will make obsolete most university professors that teach the first four semesters of physics.
At the end of the story, we see a “danse macabre”, a human chain of university professors being led by the college administrator over a hill. Presumably, at the other side of the hill, the cruel fate of a non-academic job awaits them.
October 23, 2013
Google has recently partnered with a leading manufacturer of e-cigarettes to produce the first ever “e-cig mod”. The mod is targeted at those K12 youngsters who, despite their best efforts and burning desire to learn, might have been deprived of an elementary Chemistry education because of the scarcity of good introductory Chemistry resources on the web. The mod includes an attractive, multi-media, educational package explaining the Chemistry of the concoctions that go into e-cigs, plus 7 yummy nicotine additives (chocolate, Fuji apple, Bombay mango, Island coconut, vanilla, cherry, peach) that a budding scientist can experiment with without danger of poisoning him or herself, as they have been thoroughly tested by the nice Google staff, which is so wise and can do no wrong.
A Google spokeswoman said: “e-cigs are phenomenally popular among middle and high school kids. About a third of those kids are already using them. So we believe, aren’t we brilliant, that e-cigs are the best way to introduce those kids to Chemistry, and thereby produce the scientists of the future.”
When asked about Chemistry sets, the spokeswoman said: “Oh, but those are so passé. Besides, they are too dangerous. What if the kid poisons himself or puts an eye out? Do you want to have a little pyromaniac in your hands, one that revels in loud explosions and devastating stink bombs?”
(This blog post was inspired by qCraft, a mod produced by Google and Caltech of a video game called MineCraft that is currently very popular among the K12 crowd. Qcraft is intended to teach little kids quantum mechanics. Spiros posted about qCraft in the Caltech blog Quantum Frontiers. My comment to his blog post elicited quite a few thumbs-down. That’s okay. I call the up-and-down-thumbs widget in blogs, “standing on the shoulders of worms”)
October 19, 2013
I just watched a lowest-of-the-low-brow video, produced by Google, about quantum computers. Nothing but clichés stitched together illogically. The thing must have been produced by someone with the IQ of a potted plant. Its goal seems to be to explain, I know not to whom, maybe to another plant, what is quantum mechanics. To explain in lucid terms how Google will use quantum computers to disrupt AI, solve global warming, and decide whether we are alone or not in the universe. So this is how plants communicate with each other!
Oh wait! according to this blog post, the producer of this video is Spiros’ talented and handsomely paid female friend. And she and her cohorts are planning to make a video game that uses vague metaphors to confuse the hell out of little kids trying to understand quantum mechanics. Sorry Spiros. Your girlfriend’s video is a really deep film. It taught me a lot about Greek history. I just wish it had in it any information at all about the Greeks. If only your girlfriend had included some gossipy sections about Helen of Troy, Paris and Menelaus.
It’s clear from the video that Google, the company that runs the world (or is trying to, in collaboration with the NSA), is convinced that the multi-verse interpretation of quantum mechanics is the only true interpretation, the only true religion, for clearly, as David Deutsch says, the other interpretations totally fail to explain why quantum computers work. After watching the video, I came home with the impression that Google is planning to use its D-Wave quantum computers like a Ouija board to consult the multi-verse and make company decisions based on what the multi-verse tells them.
I’m not an avid fan of the multi-verse interpretation of QM. I expounded on my views about this in a previous blog post:
Not being a fan of the interpretation, I’m ill informed about its subtleties. (Steve Hsu, a real expert on it, is invited to chime in). But it seems to me that Google’s resident quantum mechanics expert, Hartmut Neven, made a mistake in his slides, which he presented in Spiros’s girlfriend’s video. Hartmut presented the following slide:
It seems to me that this slide is misleading, because if the multi-verse is going to predict anything but noise, a preponderance of universes must agree and predict what we are now seeing. In Hartmut’s slide, all possibilities are clearly not true, especially the one about Hartmut The Physicist. The lobster one is the only one that comes close, as Hartmut seems to sped too much time outdoors and his coloration definitely tends towards the reddish.
I have amended Hartmut’s slide to better represent the multi-verse interpretation.
In my slide you can see that 3 out of the 4 universes agree amongst each other and with what we, in this universe, are observing, and the fourth universe is not too far off.
By the way, my slide was inspired by a famous portrait of Lee Smolin, painted by the artist Lubos Motl. A portrait which has been burned into our collective consciousness. After having seen it just once, it’s hard for anyone to think of Lee Smolin without seeing his face surrounded by a clay pot. Lee Smolin, in case you don’t know, is a role model and poster child of PI (Perimeter Institute) and iQC (Institute for Quantum Computing).
October 12, 2013
Secret message: Operation Lisbeth is going really well.
In a previous post entitled “Life in the Time of the Bayesian Wars“, I pointed out that “Companies like IBM, Google, Oracle, HP/Autonomy and SAP are in a fierce battle for the supremacy over the Bayesian sea lanes and trade routes to the New World.” and that “quantum computers have the potential to escalate that war significantly.” (I love quoting myself. I always agree with myself completely)
One particular battle in that war, a battle that is now raging at maximum intensity, is the one over personal assistants (PAs). PAs rely on a carefully curated database of facts called a knowledge base (KB). Some of the opening salvos of the Battle of PA Hill were made by Wolfram Research with its KB Wolfram Alpha, by IBM with its PA Watson and by Apple with its PA Siri. Since those initial volleys, the war has escalated. Now two search engine superpowers, Google and Microsoft/Bing, have joined the fray. Search engine (or social network) companies have a great advantage over IBM and other analytics giants, because they are in a better position to leverage the data of web pages plus user queries and personal data. Here is what these two search engine empires call their military operations:
|Knowledge Graph||Android’s Now|
Even though it might appear that Microsoft has just joined the fight, and doesn’t stand a chance against mighty Google, the truth is that MS has been involved in the PA battle longer than any other superpower. Google was founded in 1998, but as far back as 1996, Bill Gates was already telling everyone that someday B nets would be Microsoft’s secret weapon. Microsoft’s initial entry into the field was Clippy :), not the best of starts, although the story is that the B net part of Clippy was removed or badly crippled at the last moment, so Clippy is not a true representative of B net power, thank God. More recent PA attempts by Microsoft like their “Virtual Receptionist” are much more respectable.
Recently, the Redmond giant has uttered some battle cries that must be unnerving to their opponents. Microsoft has been bragging that their KB Satori (which means “understanding” and “enlightenment” in Japanese) and their PA Cortana (named after a holographic AI in the XBox video game Halo), both of which are soon to be unveiled in their full majesty, are more advanced Bayesian weapons, true death stars, than the weapons of their competitors.
Microsoft has faltered frequently and foolishly in the past ten years (with the exception of Kinetic which is pretty cool). Will Satori and Cortana finally take Microsoft out of the doldrums it’s been stuck in for the past decade and save cash hemorrhaging Bing? Or is it all bluster on their part and once again they will end up replaying the bungling role of the Brits in the charge of the light brigade? Stay tuned.There are of course many elements to a KB and PA that have nothing to do with Bayesian analysis so some might say that us Bayesians take credit for everything. Okay, but you have to admit that important parts of the analysis done by PAs, either the current ones or the future versions, will be heavily based on Bayesian ideas.
Of course, I think a secret weapon that has the potential to change the outcome of this war is quantum computer AI. We’ll see.
Check out this nice war reportage from the front lines:
Microsoft’s Answer To Siri: Cortana, by Michael Endler (InformationWeek.com, September 13, 2013)
Cortana anticipation has been building again in recent days, after several purported Windows 8.1 images leaked online. Citing an inside source, ZDNet’s Mary Jo Foley subsequently reported that Microsoft is indeed readying a digital assistant technology, but that it will involve more than smartphones; rather, it will be a “shell” that harnesses the cloud to personalize and unify user experiences across Microsoft devices and services.
Apple’s Siri already follows voice commands and intelligently aggregates information in response to certain user queries. Android’s Google Now goes a step further in some ways; if the user chooses, it will scan emails, calendars and other data in order to learn more about the user and anticipate his or her needs. Cortana reportedly aims to outdo both competitors thanks to Microsoft’s Satori technology, which is currently used in Bing.
Bing senior developer Stefan Weitz added fuel to the fire in late July, telling CNET that Siri and Google Now “have a fairly shallow understanding of the world,” and that Microsoft will not ship a competitor until it can disrupt the market. “We could come out with something like [Siri and Google Now], but it wouldn’t be state of the art,” he said, noting that Satori’s brain is powered by more than 50,000 nodes in Microsoft’s cloud.
Microsoft founder Bill Gates and retiring Microsoft CEO Steve Ballmer also have chimed in with hints. In the memo that announced the “one Microsoft” restructuring plan, Ballmer wrote that the company’s technology “will understand people’s needs and what is available in the world, and will provide information and assistance.” He said Microsoft services will anticipate each user’s daily needs and provide insight when it’s needed.
Other great war reportage:
- Microsoft’s Bing seeks enlightenment with Satori, by Dan Farber (cnet.com, July 30, 2013)
- Microsoft’s Cortana to Battle Siri, by Pedro Hernandez (eweek.com, 2013-09-12)
October 2, 2013
The squashed entanglement of a quantum channel
(http://arxiv.org/abs/1310.0129) by Masahiro Takeoka (1,2), Saikat Guha (2), and Mark M. Wilde (3)
- National Institute of Information and Communications Technology, 4-2-1 Nukuikita, Koganei, Tokyo 184-8795, Japan
- Quantum Information Processing Group, Raytheon BBN Technologies, Cambridge, MA 02138, USA
- Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA
This is one in a long series of papers that lie about the origins of Squashed Entanglement. The paper attributes the invention of squashed entanglement to Christandl and Winter. This is an outright lie, as one can easily establish by consulting arXiv.
As the Wikipedia article on squashed entanglement clearly documents, giving pertinent arXiv references, I had submitted to arXiv about 5 papers on squashed entanglement, giving the EXACT modern definition, and I had even written a C++ computer program to calculate it, about 3 years before Christandl-Winter wrote their first paper on it. (although I didn’t call it squashed entanglement, I just called it a generalization of the definition given by Bennett, et al. of entanglement of formation for mixed states, not a very catchy name I must admit, although I don’t think the name squashed entanglement is much of an improvement). I had also sent email to Winter pointing out my papers to him before he wrote his paper with Christandl about squashed entanglement.
It seems that Masahiro Takeoka, Saikat Guha, Mark M. Wilde are doing this to hurt me because they are dumb, unethical, nasty thugs. They are too dumb to realize that their paper in no way detracts from my work. All their paper does is to hurt their own reputation, by giving tangible evidence that they are dishonest scientists and immoral people. And now that this paper is on arXiv, this evidence will follow them for eternity. The duration of the punishment is extremely harsh, but it’s not my fault. Blame Paul Ginsparg, main arXiv inventor (?), for it
September 28, 2013
One of the simplest applications of Grover’s algorithm is to calculate the average of an unstructured function. Let me explain one way of doing this.
Let with for all . Thus is just a string of bits. Suppose we want to find the average of a function that maps each to a real number. In other words, we want to find
This can also be interpreted as the integral of over the space of all . We will assume the function is bounded above and below: i.e., for all , there exist reals such that . Then replace by the more convenient function which satisfies for all , and .
Let label distinct qubits and an extra single qubit.
We will assume that one can construct the following “target" state using poly(n) number of steps:
where is some real number and is some normalized state. For to be normalized, we must have so
To find , one can use Grover's algorithm (or better still, my home-brewed version of Grover's algorithm, what I call AFGA. Unlike plain Grover's algorithm, AFGA always converges exactly to the target without overshooting). AFGA converges in order steps. For our “starting" state , we will use:
where is some bit string for which .
so the AFGA converges in order steps. By comparison, classical averaging takes order steps if is unstructured.
Finally, note that
Hence, if we ignore the qubits and only measure the one, and if and are the number of zeros and ones respectively that we measure for , then
There are other ways of finding using Grover's algorithm. One way was given by Grover. Later, Brassard, Hoyer and others found alternative ways. Here are some references:
- “A Framework for fast quantum mechanical algorithms”, by Lov Grover, http://arxiv.org/abs/quant-ph/9711043
- “Quantum Amplitude Amplification and Estimation”,
G. Brassard, P. Hoyer, M. Mosca, A. Tapp, http://arxiv.org/abs/quantph/0005055
- “An optimal quantum algorithm to approximate the mean and its application for approximating the median of a set of points over an arbitrary distance”, by G. Brassard, F. Dupuis, S. Gambs, A. Tapp, http://arxiv.org/abs/1106.4267