To be more precise with the analogy: resolution in physics is roughly equivalent to block height in Bitcoin. The longer your local copy of the timechain, the more information (resolution) you possess. So, implementing Shor’s algorithm to break a sufficiently large key would be analogous to performing a large amount of PoW (an entropy cost) in physics, not something you get for free through quantum error correction magic. In short, it would require a significant amount of energy to flatten the effective local wavefunction enough to solve large problems.