A scalable, modular, fault-tolerant quantum computer based on Rydberg arrays and optical cavities

One of the most promising routes toward scalable quantum computing is a modular approach. We show that distinct surface code patches can be connected in a fault-tolerant manner even in the presence of substantial noise along their connecting interface. We quantify analytically and numerically the combined effect of errors across the interface and bulk. We show that the system can tolerate 14 times higher noise at the interface than the bulk, with only a small effect on the code's threshold and sub-threshold behavior, reaching threshold with ~1% bulk errors and ~10% interface errors. We apply these results to the specific case of programmable Rydberg arrays, proposing a novel architecture for quantum computing which is scalable, modular, and fault-tolerant. Differing from previous modular approaches, our modules are large, containing hundreds to thousands of qubits forming surface code patches linked together using only modest quality Bell pairs. To analyze the feasibility of our architecture, we further develop detailed workflows and give quantitative performance estimates showing that a single optical cavity of modest quality allows Bell pair distribution fast enough to realize 10 kHz surface codes, much faster than current coherence times.