I think that the teaching of QM has already been impacted by quantum information—and I hope it gets impacted more, regardless of if and when we get useful QCs! To my mind, it’s just infinitely clearer to start with the basic rules and properties of QM—states, unitary transformations, measurements, tensor products, entanglement, density matrices, etc.—illustrated with the simplest systems to which those rules apply, namely collections of qubits (or more generally, finite-dimensional Hilbert spaces). This already lets the students fully understand no-cloning, quantum teleportation, quantum key distribution, basic quantum algorithms like Bernstein-Vazirani and Simon, and other cool things from quantum information, and it already lets them explore the conceptual questions (the measurement problem and so forth) that interest most of them. After this material has been mastered, and only after, one could see how it gets applied to real physical systems like the harmonic oscillator, the hydrogen atom, or a particle in a 1D potential well. So, all the mathematical complications of infinite-dimensional Hilbert spaces—which are not essential to understanding QM itself—could be deterred to this part of the course. This is the reverse of the historical order in which the ideas were discovered in the 1920s, but I think it’s the much more logical order in which to learn them—even if quantum information weren’t a big thing that people now care about.

If you want to see a recent text by a bona fide physicist that presents QM in exactly this way—what I think of as simply the “modern” way—then check out Lenny Susskind and Art Friedman’s remarkable “The Theoretical Minimum” series. Or you could look at pretty much any introductory book or course lecture notes about quantum information, including mine. We do it this way as well, except that we never do get to the harmonic oscillator or the hydrogen atom. :-) I can say from experience that the material is then totally accessible to any bright undergrad who’s done math up through linear algebra.