Historically, quantum theory evolved as a microscopic theory of matter. Important milestones included the discoveries of the wave-nature of matter, interference phenomena, the uncertainty principle, and the level structures of atoms and molecules. In the non-relativistic realm, the mathematical centerpiece of this theory of matter is the Schrödinger equation (later extended to account for spin and particle statistics). It is this body of theory which dominates the teaching of quantum mechanics to the present day. More recently, however, an alternative paradigm has emerged which is gaining ever greater importance: that of quantum theory as a framework for information processing. It allows one to talk about qubits and to devise information processing protocols without ever caring about the underlying material substrate. While this is now also taught in many courses, these are mostly supplementary or specialized graduate courses that build on the conventional introductory courses on quantum mechanics. Rarely, if ever, is the new information processing paradigm already incorporated into the standard introductory course itself. I find this to be a pity, for several reasons:
- Describing qubits and their manipulation requires only minimal mathematics. It allows thus a very simple, direct route to interesting quantum phenomena. By contrast, much of conventional quantum mechanics is dominated (and, arguably, obscured) by complicated mathematics, such as the theory of partial differential equations.
- For the same reason, the information processing approach allows one to go straight to the heart of some of the most interesting conceptual issues in quantum theory, such as the Bell and Kochen-Specker theorems.
- Since it is does not require prior knowledge of classical physics or advanced mathematics, the information processing approach to quantum theory may be taught earlier in the curriculum and even to students in other fields, such as mathematics, computer science, or engineering.
- With more and more research institutions and corporations joining the development of quantum technologies, there is a growing need for graduates trained in quantum information processing. In order to meet this greater demand, it will be necessary to bring quantum information processing into the mainstream of teaching and to make it a central part of every introductory course on quantum mechanics.
I am currently working on a quantum theory textbook that aims to turn the conventional teaching approach on its head: It will start with quantum information processing and lead to the theory of matter, rather than the other way round. Specifically, it will feature the Schrödinger equation only at the end, rather than at the beginning. Since I am still fleshing out the details, I would like to engage with you in an open discussion about the best structure of such an approach. Compared to a conventional introductory course, which new topics should be added? Which traditional topics can be left out? What is the best line of reasoning that leads from quantum information processing to the theory of matter (which, after all, will still have to be taught)?