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

Abstract

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(log2R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m=O({\log }^{2}R)$$\end{document} 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=Ω(logR)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m=\Omega (\log R)$$\end{document} qubits per repeater.