## Why a national initiative in quantum information is needed

I recently read an article on cyberspying in *The Week* and it got me thinking again about the need for advancement in quantum information science. Back in November I wrote about legendary cyber security expert Bruce Schneier’s pronouncement about quantum cryptography. Schneier believes present security protocols such as RSA are secure enough to ward off any attack using existing technology. If that were true, why are such things not addressed in the article on cyberspying? At the close of the article, British computer scientist Ross Anderson is quoted as saying “It takes a professor of computer science to have the confidence to say that some things simply should never be put on a computer.” (In itself, this is an argument against the push toward cloud computing.)

In other words, while RSA may be nearly perfectly secure against attacks by classical computers (and assuming quantum computers are still a ways away), there are other factors that come into play when dealing with electronic security such as human nature, economics, etc. For instance, a few years ago (2007) there was a classic man-in-the-middle attack on a data stream containing credit card information for customers of a major supermarket chain here in New England. The data stream *wasn’t encoded*. When this was leaked a lot of people wondered why, in this day and age, it wouldn’t be. The answer is that, when transmitting huge chunks of data, it is often impractical to encode the whole thing since it tends to increase the size of the data chunk. Now, a quantum system won’t necessarily solve this particular problem, but it can help.

In terms of quantum cryptography, which is more accurately known as quantum key distribution (QKD), the quantum part is used to create the key that is used to encode the data. As such, this does not necessarily solve the problem, by itself, of reducing the excess data in order to make it more easily transmittable. In fact, technically, it is impossible to encode any more than one classical bit in a single qubit. However, if an entangled pair of qubits is shared by the sender and receiver, it is possible to actually increase the efficiency. This process is known as *superdense coding*. “Ah, but,” you say, “that requires a noiseless channel!” OK, so now you see the need for a greater understanding of fault-tolerance and error-correction. In other words, all the little sub-sub-fields of QIS are interrelated.

“Alright, alright,” you continue. “I get that all this QIS stuff goes together. But quantum computing is so far off that I can’t see investing heavily in it just yet.” Ah, but you have fallen into the trap of assuming that ‘quantum information’ is synonymous with ‘quantum computing.’ It isn’t. More appropriately one should think of the latter being somewhat like a branch of the former. While we may be decades (or maybe only years – who knows) away from a practical quantum computer, we already have usable commercial quantum crypographic devices. There is much more progress that needs to be made before this stuff can be used in day-to-day situations such as the supermarket fiasco, but enough technology and associated knowledge exists that a national initiative could make some major technological progress possible in the near future. In addition, quantum cryptography is perfectly suited to fiber optic communications, something that is increasingly overtaking traditional electronic techniques worldwide (specific capacities are proprietary, but as of 2002 there were supposedly 250,000 km of undersea fiber optic lines). It is also being tested in free-space transmissions (i.e. satellite uplinks, etc.).

So, in summary, while present encryption methods may be perfectly secure against classical attacks when used properly, they suffer from a number of implementation problems related to economics, existing technology, and plain old human nature. In other words, Bruce Schneier’s comment was a bit simplistic. Quantum processes overcome some of these problems and with a strong national investment in quantum information science such as that discussed at a recent meeting Virginia, we can achieve truly, reliably secure data transmission and storage while mitigating some of the problems associated with the usual classical methods.

June 10, 2009 at 6:46 pm

I’ll be the first to comment … Ian, this is a fine essay!

I’ll ask a pedagogic question (since you are math department chair) what level of mathematical education is needed to turn these ideas into hardware?

And how many engineers and scientists are we graduating, who have the necessary mathematical training to make QIT/QIS work in the private sector?

June 10, 2009 at 9:53 pm

Wow, John, that second one is a seriously tough – but excellent – question. I think there may not be a single right answer to it, either. As for the first question, I think it depends on the approach we take. Simple quantum cryptographic protocols require nothing more than linear algebra which all undergraduate physics students likely have had, though the same may not be true for engineers (I took it as an undergraduate mechanical engineer, but it was by choice).

Personally, I think there needs to be a revamping of undergraduate algebraic education in that a little bit of category theory needs to be brought in. It’s already used in some computer science situations and is becoming increasingly important in QIS.

So, ideally, I would want a non-mathematician working in QIS to have had linear algebra as well as a basic group theory course (and you could theoretically squeeze some category theory into the latter towards the end). I suspect that is probably sufficient for implementation of anything we’re talking about here.

Now, I’m pretty certain most physics departments require linear algebra (they should – we certainly do here at Saint A’s). I would guess that a good number of engineering departments do as well (it only makes sense), though it is likely less ubiquitous than in physics. I would bet that the group theory material is almost never required of anyone but mathematicians. We have tried to cajole a few of our physics majors into taking that class (particularly this spring when I was the one teaching it), but we haven’t had many takers yet. It’s pretty abstract and it is often difficult for students to see how applicable it is (which is why I try to bring in real-world applications when I teach it).

In any case, thinking off-the-cuff here at 11 PM while my eyes droop, I would hesitantly say that linear algebra is sufficient at this point and that most engineers and physicists have had it. But in the near future, I see an increased need for a better understanding of more abstract algebraic methods as well as the need to understand how to physically implement some of those methods. As an example, a paper I just put on the arXiv has an interesting category theoretic conclusion concerning quantum channels. But the question remains: how could we implement something like this? I think there is a way, but some very creative and knowledgeable engineers are needed for things like this.

In short, I have no idea if I have given a satisfactory answer, but I would be very interested to hear what other people have to say about this. I think it is a point worth debating particularly in relation to any discussion of a national QIS initiative.

June 11, 2009 at 10:32 am

Ian, I am completely in agreement with you as to category theory. And another emerging professional requirement (in modern engineering) is exposure to the basic tools of manifold theory + differential geometry + algebraic geometry (which obviously overlap with category theory).

The reason is that nowadays, pretty much every major scientific experiment and/or engineering design project includes an end-to-end simulation, and that simulation is almost always (nowadays) computed on a manifold rather than a vector space (as in the past).

For example, in QIS/QIT most large-scale calculations are done (nowadays) on a tensor network state-space, which is *not* a vector space.

Fortunately, category theory + manifold theory + differential geometry fit together exceedingly well — I think Bob Geroch’s

Mathematical Physicswas one of the first (and best) textbooks to adopt this framework.In our own QSE Group seminar, we’ve been using Geroch’s framework to condense the key points of Nielsen and Chuang’s textbook down to a one-page sheet of practical simulation recipes:

http://faculty.washington.edu/sidles/QSEPACK/Kavli/QSE_summary.pdf

The pedagogic challenge is, the mathematical terminology of this one-page summary is not covered in undergraduate courses … and yet, once a student starts graduate school, specialization begins almost immediately.

The result is that nowadays, too-few students in math, science, or engineering are acquiring what Bill Gasarch calls “the ever-elusive mathematical maturity” that is required to approach modern engineering and science in an integrative way.

All this boils down to a simple question: how can we do a better job of fostering “mathematical maturity” in our math/science/engineering students?

In medicine, the analogous quality is called “clinical competence”, and I can tell you exactly how we foster it: ten years of post-graduate education (four years in med school and six in residency) with a one-to-one faculty/student ratio!

Obviously a medical-style educational environment is not feasible in math/science/engineering. Because the traditional four-year curriculum is full! That is why (IMHO) a good start would be for engineering degrees to be six-year degrees, with the extra two years wholly devoted to developing “mathematical maturity” and “system engineering maturity”.

June 11, 2009 at 8:20 pm

John, this is very interesting. Thanks for bringing my attention to Garoch’s book. I’d never heard of it before. We’ve been looking to revamp our math physics course for awhile.

I am a big believer in developing the mathematical maturity of our students and I’m hoping to convince others of this. Personally I think this extends well beyond the sciences and, unfortunately, that is a serious weak point of Saint A’s (and many schools). We have no general math requirement. We are seriously considering changing this, but the practicality of it is daunting to the administration, not the least because of the monetary investment it would require in order to hire new faculty.

In any case, this should be incorporated into any national initiative in QIS. Frankly, it seems as if it ought to be something addressed in physics and engineering in general. With the latter, the push could come from ABET, but I don’t know how one could successfully push physicists into a wholesale change. Getting physicists to agree on anything is like trying to herd cats.

I agree with your take on engineering degrees as well. I spent five years on my mechanical degree back in the early ’90s. Even then there were very few engineers who finished in four years.