Theoretically, if we had a GPU so fast it could instantly calculate billions of digits of Pi, and a small hard drive, could this actually be made to work?

Cache all the last lookups but otherwise just store the index within pi? And for larger files - split them into chunks of whatever size could be handled?

(I mean, I realize this is a joke and can't make sense - but GPUs can be really really fast, and am willing to make a fool of myself by asking.)

And if we had a quantum computer that stores all of pi on one qubit, that could make things even faster ;/