Quantum coding with low-depth random circuits

We study quantum error correcting codes generated by local random circuits and consider the circuit depth required to achieve high-performance against local error models. Notably, we find that random circuits in D spatial dimensions generate high-performing codes at depth at most O(log N) independent of D. Our approach to quantum code design is rooted in arguments from statistical physics and establishes several deep connections between random quantum coding and critical phenomena in phase transitions. In addition, we introduce a method of targeted measurements to achieve high-performance coding at sub-logarithmic depth above one dimension. These latter results provide interesting connections to the topic of measurement-induced entanglement phase transitions.

Reference: Gullans, Michael J., et al. "Quantum coding with low-depth random circuits." arXiv preprint arXiv:2010.09775 (2020).