general QC applications are well-known
The applications of quantum computing are still a little handwavy at the moment
I don't believe they are. The likelihood of practical general QC may be very much in doubt,1 but if we ever have it, we know what to do with it. There are two very well-known, general-purpose algorithms in BQP (Shor's and Grover's), and they have a bunch of practical applications. The other big area is in physics simulations.
The more interesting question (besides the feasibility one, on which I am skeptical) is economics. If GQC does turn out to be "practical" but only at tremendous resource cost, then will any problems be worth using it? We already have trial deployments of post-quantum cryptography for mass crypto (i.e. TLS),2 so by the time anyone has a usable GQC machine it'll only be useful for cracking historical cryptography; and if it's expensive, only very select items from the archives.3 For other applications, you'd have to find specific instances of problems where those specific solutions have great value.
Physics simulations look like the most plausible applications for Really Expensive General Quantum Computing.
1And, no, the DWave machine does not count. That may not be quantum anything, and even if it is, it's just adiabatic QC (quantum annealing). It's a fancy analog computer, with of course a big classical digital computer wrapped around it. It doesn't solve problems in BQP.
2Google's rolling out their second experimental post-quantum TLS suite, using a combination of X25519 and HRSS for Kx.
3The lack of PFS with RSA Kx means more bang for your buck when cracking the key exchange in most of the archived SSL/TLS traffic the NSA and other SIGINT types are no doubt holding, but you'd still have to identify targets of great interest if cracking is expensive. And a lot of that we can crack with conventional machines now, if we really want to.
Biting the hand that feeds IT
