> I have not seen even a theoretical framework allowing both to be increased simultaneously.
The threshold theorem [1], showing this can be done in principle, was proven more than a decade ago.
But you don't have to believe the theory anymore, there's experiments now! Last month the google quantum computing team published an experiment [2] showing memory error rates (including decoherence) getting twice as good as a surface code was grown from distance 3 to distance 5, and twice as good again going from distance 5 to distance 7. The logical qubit's coherence time was longer than the coherence times of the physical qubits it was built out of.
The threshold theorem [1], showing this can be done in principle, was proven more than a decade ago.
But you don't have to believe the theory anymore, there's experiments now! Last month the google quantum computing team published an experiment [2] showing memory error rates (including decoherence) getting twice as good as a surface code was grown from distance 3 to distance 5, and twice as good again going from distance 5 to distance 7. The logical qubit's coherence time was longer than the coherence times of the physical qubits it was built out of.
[1]: https://en.wikipedia.org/wiki/Threshold_theorem
[2]: https://arxiv.org/abs/2408.13687