Sublime Superlemon

I wrote the article below for a newsletter called “Quantum Information Times”. I know it has nothing to do with baking which is why I must commit myself to posting something more delicious soon. (Also, as a quick note, photo credit goes to this person: http://www.flickr.com/photos/jaz_q6r/2596262040/)

The Bachelor in Quantum Information Science and why it won’t happen

Jan Florjanczyk

Doubtlessly, quantum information has benefited by assimilating members trained in a wide array of sciences, predominantly physics, mathematics and computer science. However, with (im)perfect 20/20 hindsight, we can always speculate on what a specialized undergraduate degree in quantum information science may look like.

The transition from the undergraduate curriculum-led lifestyle to the graduate research-led one can be turbulent when headed for quantum information. Likely, students come from at most two of the above three constituent areas. As a graduate student you can always play the game of “picking things up as you go” but this is not a mentality that scales well to the average freshman. Learning to trace results up through their parent papers or even searching the Internet using correct terminology is tough to learn in a lecture hall. To students starting out, the field of knowledge ahead of them seems of an absolutely overwhelming size. Thus, to make a quantum information scientist from scratch we have to examine what is essential and what is superfluous in an undergraduate curriculum.

Personally, I come from a background in physics and mathematics so I can only speak from this vantage point. However, my recent foray into computer science has shown me very clearly what it is that I lacked (or likely still lack) in that field. Altogether, I’m looking to distill in this article the essentials from my undergraduate degree that now support my studies in quantum information.

The core of the mathematics required is a basic understanding of probability and a very strong foundation of linear algebra. With only these tools we already find ourselves with enough framework to begin proving some rudimentary results. However, a course in probability at the undergraduate level is likely to focus on a survey of distributions and characteristic functions. We can make due with Bayes’ rule and Markov’s inequality in our curriculum. Alongside a short survey of constructions such as cyclic groups, a thorough understanding of linear algebra plays the central role in quantum information theory. More particularly, it is essential to grasp tensor product structure early on and this is very easily overlooked in a math program. Also, I would urge to prescribe the full run of mathematical analysis courses. Knowing about metric spaces and measure theory has proven repeatedly useful. Finally, group theory, complex variables and PDEs belong in this program as well, but a thorough treatment is not necessary as a student can still follow along most of the material without them.

A “classical” physics program is also a little ill-at-ease in the shaping of a quantum information scientist. Newtonian and (I would claim) Hamiltonian mechanics simply never appear. Classical electromagnetism and optics can lead to quantum optics so perhaps they should be included. But what else is left? Statistical mechanics and quantum mechanics, both of which tend of play off each other a little. Quantum mechanics itself deserves the most attention. The practice is to divide a large survey of quantum mechanics into two or three successive courses. These begin with introductory topics such as the Schroedinger equation, potential wells, eigenstates and values (all strictly in one spatial dimension). Next, students find themselves solving the equations of the hydrogen atom. For this they need spin operators, variational methods and most importantly: perturbation theory. Density operators may make a brief appearance in the third course and although Bell measurements may be mentioned, the POVM formalism is generally ignored. The process of teaching successively complicated mathematical methods to support successively complicated physical scenarios makes sense to enforce a more phenomenological understanding of physics. However, this is the long way to get to what quantum information science really needs, that is, a foundational understanding that leads to the circuit model necessary for algorithm development.

Enter the third science. The most important computer science concepts I could have had coming into quantum information are definitely algorithm design and complexity theory. I am unashamed to say that as a student formerly bound for something closer to the study of general relativity, the word “algorithm” was once terrifying. Even the design of the simplest algorithms is not a “pick it up as you go” affair. It is just as practiced an art as any problem solving in mathematics and physics. The computer science component of this curriculum must also provide a course in information theory. This is essential because although you can sit down and read the classical background from Mike and Ike, there’s no way to develop intuition without practice.

The only missing piece is a course (or a few courses) in quantum information proper. Any of the textbooks suggested by Mark Wilde (above/below) could be suitable. However, if you try to solidify a point at which to teach quantum information with respect to its math, physics, and computer science requisites, you cannot do so honestly until very late in the program. For example, it is difficult to introduce the Hadamard gate without quantum states, which in turn cannot be introduced until a solid understanding of linear algebra is established. Whichever way you go about it, you would always end up pushing the quantum information content further and further back in the program until you reached something resembling more of a B.Sc. (Hons. in QIS) than a true Bachelor in Quantum Information Science.

Perhaps it is fortunate that diving immediately into quantum information out of high school is impossible. Students in their undergraduate years change direction very often. A program specific to quantum information would be restricting since it would provide only background required for QIS and lack in the overlap required for students to move subjects. Quantum information science also gains much by attracting diversely educated students. Every math, physics, and computer science course that was not mentioned here plays a vital role in shaping the individuals who make up the QIS community. Nor should it be forgotten that chemistry and engineering are also contributors to the rapidly spreading pool. All in all, a Bachelor in Quantum Information Science would accomplish nothing more than guide a student through the history of quantum information science but sadly leave them short-handed for research in the field.

For now we can just wait until the game-changer: a fully functioning quantum computer. At that point we can start to visit the exciting realm of the Bachelor in Quantum Engineering.