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

We propose a scheme for fault-tolerant long-range entanglement generation at the ends of a rectangular array of qubits of length $R$ and a square cross section of size $d\times d$ with $d=O(\log R)$. Up to an efficiently computable Pauli correction, the scheme generates a maximally entangled state of two qubits using a depth-$6$ circuit consisting of nearest-neighbor Clifford gates and local measurements only. Compared with existing fault-tolerance schemes for quantum communication, the protocol is distinguished by its low latency: starting from a product state, the entangled state is prepared in a time $O(t_{\textrm{local}})$ determined only by the local gate and measurement operation time $t_{\textrm{local}}$. Furthermore, the requirements on local repeater stations are minimal: Each repeater uses only $\Theta(\log^2 R)$ qubits with a lifetime of order $O(t_{\textrm{local}})$. We prove a converse bound $\Omega(\log R)$ on the number of qubits per repeater among all low-latency schemes for fault-tolerant quantum communication over distance $R$. Furthermore, all operations within a repeater are local when the qubits are arranged in a square lattice. The noise-resilience of our scheme relies on the fault-tolerance properties of the underlying cluster state. We give a full error analysis, establishing a fault-tolerance threshold against general (circuit-level) local stochastic noise affecting preparation, entangling operations and measurements. This includes, in particular, errors correlated in time and space. Our conservative analytical estimates are surprisingly optimistic, suggesting that the scheme is suited for long-range entanglement generation both in and between near-term quantum computing devices.
Comment: 68 pages, 11 figures