Long-range data transmission in a fault-tolerant quantum bus architecture

We propose a fault-tolerant scheme for generating long-range entanglement at the ends of a rectangular array of qubits of length R with a square cross-section of $m=O\left({\log }^{2}R\right)$ qubits. It is realized by a constant-depth circuit producing a constant-fidelity Bell-pair (independent of R) for local stochastic noise of strength below an experimentally realistic threshold. The scheme can be viewed as a quantum bus in a quantum computing architecture where qubits are arranged on a rectangular 3D grid, and all operations are between neighboring qubits. Alternatively, it can be seen as a quantum repeater protocol along a line, with neighboring repeaters placed at a short distance to allow constant-fidelity nearest-neighbor operations. To show our protocol uses a number of qubits close to optimal, we show that any noise-resilient distance-R entanglement generation scheme realized by a constant-depth circuit needs at least $m=\Omega \left(\log R\right)$ qubits per repeater.