Longrange data transmission in a faulttolerant quantum bus architecture
Abstract
We propose a scheme for faulttolerant longrange 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 nearestneighbor Clifford gates and local measurements only. Compared with existing faulttolerance 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 lowlatency schemes for faulttolerant quantum communication over distance $R$. Furthermore, all operations within a repeater are local when the qubits are arranged in a square lattice. The noiseresilience of our scheme relies on the faulttolerance properties of the underlying cluster state. We give a full error analysis, establishing a faulttolerance threshold against general (circuitlevel) 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 longrange entanglement generation both in and between nearterm quantum computing devices.
 Publication:

arXiv eprints
 Pub Date:
 September 2022
 arXiv:
 arXiv:2209.09774
 Bibcode:
 2022arXiv220909774C
 Keywords:

 Quantum Physics
 EPrint:
 68 pages, 11 figures