A lower bound on the overhead of quantum error correction in low dimensions
Nouédyn Baspin, Omar Fawzi, Ala Shayeghi · arXiv (Cornell University) · 2023
We show that a quantum architecture with an error correction procedure limited to geometrically local operations incurs an overhead that grows with the system size, even if arbitrary error-free classical computation is allowed. In particular, we prove that in order to operate a quantum error correcting code in 2D at a logical error rate of $δ$, a space overhead of $Ω(\sqrt{\log(1/δ)})$ is needed for any constant depolarizing noise $p > 0$.