Icons for Quantum Network Nodes

 The set of icons we created for quantum network nodes, for use in network diagrams, simulators, etc., are available Creative Commons license. Use and share! Communication will be simpler if we all use the same icons. It will be easier for others to quickly grasp what we mean when we show them a diagram.

PNGs with either white or transparent background are available at https://github.com/sfc-aqua/quisp/tree/master/Network%20icons.

For My Nephew

 My nephew just finished his frosh year in college, and wants to study...astrophysics?  Not entirely sure yet, but the college where he is has only a basic physics degree anyway. He seems a little lost on what to study, so this posting is a personal one, for him, but feel free to read on if you're in the same situation.

Okay kiddo,

It sounds like you have done the basics of mechanics and geometric optics, but I'm not actually sure what else in physics. I know you haven't done Maxwell's equations and quantum mechanics, but what about special relativity and introductory thermodynamics (statistical physics)? And in math, I know you've done "calculus", by which I gather you mean functions, limits, and integration and differentiation of a single variable. Good start, but we've got a long ways to go.

Despite our conversations, it seems like you don't have a clear picture yet of the curriculum, or even the broad structure of knowledge, in math and physics.  (And since I'm a computer engineer, all of this is from that perspective, of course.) So the first thing to do is to get oriented on what you really need.

Here are a few things to help you understand the structure of the body of knowledge, which should help you figure out what classes to take (or what to study on your own).

• The Map of Mathematics. I'm sure I've recommended this before, but watch it again.
  
• The Map of Physics. Same folks, same recommendation.
  
• Map of Computer Science. (Getting the idea yet?)
  
• A #QuantumNative Engineer's Bookshelf. For you, focusing on the math and physics parts will be helpful.
  

Mathematics

For a basic physics degree, you are going to need the following math:

• Linear Algebra. Multiplying vectors and matrices, solving systems of equations via Gaussian elimination, linear and affine transformations, and eigenvalues and eigenvectors, at least. You'll also be exponentiating matrices ($e^A$, where $A$ is a matrix) in quantum mechanics, and that's easiest if you can diagonalize a matrix. You can start with my linear algebra videos, but there are lots of resources on the web. I recommend the Georgia Tech Interactive Linear Algebra online, interactive textbook. That's pretty deep, you won't need it all right away, but it's there for a reason. There is also an entire 20-hour lecture course posted as two videos in YouTube, by Prof. Jim Hefferon; I haven't watched it, so I don't know how good it is, but the comments and likes are very positive. Khan Academy has an LA course. 3 Blue 1 Brown is one of the best things on the web, and they have Essence of Linear Algebra available (full course here). In short, there are many excellent, free resources available.
• Probability, both discrete and continuous. Probability distributions, conditional probability, Bayes' Theorem, moments of distributions. For continuous, you'll need integration, so continuous comes after basic calculus.
• Statistics. I think most physics majors get away with just what they learn in a probability class unless they specialize in statistical mechanics and thermodynamics.
• Ordinary differential equations (ODEs). You said you've seen that $f'(x) = f(x)$ is solved only by the function $f(x) = e^x$, so you've seen the start of a very deep field.
• Partial differential equations (PDEs). Next step: derivatives in multiple dimensions. These are equations involving symbols like $\frac{\partial x}{\partial t}$. I first hit this when doing Maxwell's equations; I think it's pretty common for that to happen, but it means you're dealing with both a new math tool and important ideas in physics at the same time, so studying basics of PDEs first is a good idea.
• Transforms and signal processing are a big deal; you might run into Fourier, Laplace, Z and other transforms. (This is different from the linear and affine transforms above.) Often, these are tools for solving ODEs or PDEs, and might show up in an Applied Math class in your college.
• Later, you might get into more specialized topics like number theory, group theory, and graph theory. Group theory, for example, shows up in particle physics. The basics of graph theory you can learn very early, actually, and they are critical in computer science but maybe not as much in physics.

I'm sure you can find as much stuff on the later topics as I found for LA.

Physics

Surprisingly, I'm a little less comfortable talking about what basic physics you should study. Let's talk first about optics, since it's one of my favorite parts of physics, demonstrates broadly useful concepts, and happens to be what we are working on for our quantum communications research.

From among the courses we have created already, if you want the basic physics, and to minimize the quantum communications portions, these steps would be very good follow-on to your work on geometric optics. They are a bit idiosyncratic relative to an ordinary course on optics, naturally focusing on what we need for quantum communications, but they will still carry you a long way.

• OQC, Lesson 5: Coherent Light and Single Photons, leading up to a quick quantitative intro to lasers.
  
• OQC, Lesson 6.1-6.2: Interference, group and phase velocity quick introduction to constructive and destructive interference and the notions of group and phase velocity, a distinction that is crucial to understand.
  
• OQC, Lesson 7: Waveguides discusses the most important means of guiding light, of which the most famous type is, of course, optical fibers. Total up to here is about two hours worth of video, you can do this in the time it would take you to watch one soccer match.
  
• And then most of our entire module From Classical to Quantum Light, which is about 10 hours of material covering wave equations, Fourier analysis, Maxwell's equations governing how electromagnetic waves work both in a vacuum and in materials, and then into more on single photons and the like, including how detectors work. You might want to taper off when you get to the single photon stuff and defer that for after you have had basic quantum mechanics, so let's say you should do the first ten lessons of that, 45 minutes each, so about 7.5 hours.
• Among the remaining important topics to learn about are how holograms work, more on polarization, and a lot about antenna design. A good optics course will cover these things.

From the above video on the map of physics, you should have some idea of the basic list of topics:

• mechanics
• waves
• optics
• special relativity
• electricity & magnetism
• introductory quantum mechanics
• thermodynamics

That much you should take as an engineering or physics student of any sort. If you major in physics, you'll add advanced QM, particle physics, general relativity and some other topics to that list.

Given your interest in soccer, you might consider studying biomechanics, which is a bit of a specialized area and interdisciplinary, so a little biology will help, too. You should check out Professor Ohgi's Sports Dynamics and Informatics Lab as a possible destination for grad school. He works with people up to the level of Olympic athletes to understand the forces and dynamics of athletic performance. Studying some computer science before joining his lab would also be helpful.

Enough for now. Go watch those introductory things to get oriented, then study some linear algebra and probability while you watch our online courses on optics and quantum computing and communications.

Spelunking CACM, vol. 9 (1966): Eliza (and now 2022's LaMDA)

 Eliza has arrived. Eliza, who is a few months older than I am, is inarguably one of the seminal events in computing history. It's just about the only program created in the 1960s that most of us can still spontaneously name. It helped to spur my own interest in computing.

My first computer was a Radio Shack TRS-80 Model I. I also got a book with programs in it, which meant copying the programs in by hand. (Good training for catching syntax errors!)  One of those programs was called Eliza, though I suspect the BASIC version in my book was pretty different, and probably much simpler, than the 1966 version created by Joseph Weizenbaum in SLIP, a language adding list processing features to FORTRAN.

Eliza works by parsing input text into tokens and finding an important phrase (where phrases are delimited by commas or periods) based on the key word in the phrase, using a list of important words that was created by hand. Then it replaces the primary verb or subject in the phrase with one of a set of stock phrases. If you type in "I love my dog," Eliza might respond, "Tell me why you love your dog." Does mean it has any idea at all what a dog is, it just found a simple pattern and followed it.

My TRS-80 was at home, but the high school also had one, and friends of mine also enjoyed playing with Eliza. And what do high school boys want to talk about? Sex and scatalogical things and bad language, of course. You could make Eliza say some pretty hilarious things that way, by the standards of high school boys.

And now, 56 years later, we have a Google engineer and AI ethicist arguing that an intellectual descendant of Eliza has become sentient.

Chat bots have evolved tremendously since then, and are generally connected to a backend system of some sort, so that they can provide airline assistance or what have you. Often, they are connected to a neural net-based AI both for parsing the language and creating the responses. Generally speaking, no one believes they are actually sentient, but the responses will sometimes appear so insightful that your hair stands up on the back of your neck.

My skeptic's nature and my own very limited experience with chat bots cause me to lean toward siding with the Googlers who said there is no evidence that it's sentient, and plenty of evidence against it. But we are now clearly entering the realm where it will get harder and harder to tell, and the stakes of the arguments will continue to grow. Research into AI ethics grows more crucial every day.

Spelunking CACM, vol. 8 (1965): debugging, peephole optimization, and an undergraduate curriculum

(Click on the image if it isn't large enough to read.)

Overall, 1965 seemed like an "ordinary" year at CACM. I didn't see any papers that really caught my eye as some sort of extraordinary event. (Stay tuned for 1966 for that.) But there are a few things of interest, of course.

By 1965, the idea of wide-area networks was definitely in the air. Paul Baran was publishing RAND reports on the key ideas of packet switching (although I'm not sure when those became publicly available), and the ARPANET project would kick off in 1966. But connections between computers were still much more an idea than a reality, and so I.R. Neilsen had a CACM paper on a 5kHz modem for "callup" connections for exchanging medical data.

Evans and Darley presented DEBUG, which worked with other tools to allow smooth insertion of new lines of assembly while debugging a program, preventing what we now call "spaghetti code". DDT already existed for the PDP-1 at this point. I find this early history of debugging intriguing, since I have a Ph.D. student working on debugging for quantum programs now.

Maybe the most interesting trend is a pair of papers (is two enough for a trend?) on optimizing compilers. In June, Nievergelt presented "On the Automatic Simplification of Computer Programs", which proposed a set of backend techniques for individual optimizations to a stream of instructions. The paper enumerates limitations on the use of the proposed techniques, which interesting included the constraint that programs not be self-modifying, evidence that that idea was already in use.

Then in July, McKeeman gave us "Peephole Optimization". He implies that the technique is known but known and "simple" but "often neglected", and also that he is coining the term "peephole optimization" in this paper. Again implemented for the PDP-1, the explanation is clear but limited, being just over a page.

But maybe the most interesting thing as an artifact is the report from the ACM Curriculum Committee on Computer Science titled "An Undergraduate Program in Computer Science-- Preliminary Recommendations". Some earlier papers on education appeared in prior years, but I think this is the first actual organized recommendation from ACM itself. Here was the status at the time:

At the time of this writing, in the United States, doctorates can be sought at more than 15 universities, master's degrees at more than 30, baccalaureates in at least 17 colleges, and a sizeable number of other colleges and universities are presently planning or considering departments of computer science.

Impressive. I didn't know there were that many before I was born.

At the top of this post is the key table. Each of the sixteen courses there has a several-paragraph description that is well worth reading. I'm particularly intrigued that Graph Theory was already recognized as an important element in the curriculum. I am working to introduce a Graph Theory class for undergrads at our campus, for many purposes including economics, social sciences, etc., not just CS.

Each course in that table is assumed to be a U.S. 3-semester-hour course consisting of 3 hours/week x 15 weeks = 45 hours of in-class time and probably 2x that in lab or homework time for a total of, oh, 130-140 hours of work and learning. If you take just the nine "Required" plus "Highly Recommended Electives" courses, you're well over a thousand hours of time invested.  Add the seven "Other Electives", and a university that provided them all (noted in the text to be a difficult task), and you have about 2,100 hours of time. And that's not even counting the "Supporting" courses, let alone any arts and social sciences classes required. In short, this is a pretty thorough and ambitious major!

古典光学から量子光学へ

 

公開しました！

去年の「量子通信の基礎」の引き続き、「古典光学から量子工学へ」はYouTubeにアップされています。量子通信、量子インターネットなどに興味ありましたら、是非御覧ください。69本のビデオ、１０時間ぐらいがあって、以下のトピックがテーマになっている：

• 波動方程式 (wave equation)
• フーリエ分析 (Fourier analysis)
• マクスウエル方程式 (Maxwell's Laws)
• 単一光子 (quantum light and single photons)

などの内容です。今年度（つまり、来年の3月）は「量子インターネット」のモジュールを公開しますので、来年もどうぞよろしくお願いします。