There are post-quantum algorithms that are computable on ordinary computers, but they're still under research and they'd make Bitcoin's data set considerably larger.
Could you elaborate which aspect of bitcoin has efficient quantum algorithms? The proof-of-work system requires you to invert hashes and quantum algorithms only give you a quadratic speed up (brute force takes time O(\sqrt{size of range}) rather than O(size of range)). Right now there is no quantum attack on SHA-256 (which is what Bitcoin uses).
There are post-quantum algorithms that are computable on ordinary computers, ...
This sounds interesting, but could you elaborate? What does it mean for a post-quantum algorithm to be computable on ordinary computers?
BitCoin uses public key cryptography for its digital signatures. That in turn relies on the difficulty of factoring large numbers, for which there are efficient quantum algorithms.