Logical entanglement distribution between distant 2D array qubits

TL;DR

The paper tackles the challenge of distributing high-fidelity logical entanglement between distant 2D qubit arrays encoded with surface codes. It presents a concrete, tunable protocol that leverages 2D nearest-neighbor quantum channels, adaptive post-selection on estimated errors, and a rearrangement step to minimize SWAP-induced noise, followed by stabilizer-based syndrome measurements and optional post-distillation. The authors provide a detailed numerical evaluation under realistic neutral-atom parameters, showing that logical entanglement with fidelity superior to the raw physical Bell pairs is achievable, with a practical bandwidth up to about $44$ Hz for aggressive target fidelities such as $e_{\rm log} \sim 10^{-13}$. A key insight is that the acceptance threshold $w_{\mathrm thr}$ enables a controllable trade-off between protocol success probability $p_{\rm log}$ and logical error rate $e_{\rm log}$, and that post-distillation can further boost fidelity at the cost of additional trials. This work offers a feasible blueprint for scalable distributed fault-tolerant quantum computation using 2D qubit planes and motivates experimental exploration in neutral-atom platforms and beyond.

Abstract

Sharing logical entangled pairs between distant quantum nodes is a key process to achieve fault tolerant quantum computation and communication. However, there is a gap between current experimental specifications and theoretical requirements for sharing logical entangled states while improving experimental techniques. Here, we propose an efficient logical entanglement distribution protocol based on surface codes for two distant 2D qubit array with nearest-neighbor interaction. A notable feature of our protocol is that it allows post-selection according to error estimations, which provides the tunability between the infidelity of logical entanglements and the success probability of the protocol. With this feature, the fidelity of encoded logical entangled states can be improved by sacrificing success rates. We numerically evaluated the performance of our protocol and the trade-off relationship, and found that our protocol enables us to prepare logical entangled states while improving fidelity in feasible experimental parameters. We also discuss a possible physical implementation using neutral atom arrays to show the feasibility of our protocol.

Figures (5)

• Figure 1: Three steps to generate high-fidelity logical entanglements.
• Figure 2: Entanglement generation Alice and Bob perform multiplexed physical entanglement generation protocols between all the pairs of physical qubits at the same coordinate on the 2D square lattice. Since the protocol succeeds probabilistically, only a part of qubit pairs are successfully entangled.
• Figure 5: (a1, a2, a3) show the process success probability $p_{\rm log}$ in terms of the error rate of SWAP gate $e_{\rm swap}$ for configurations 1, 2, and 3, respectively. (b1, b2, b3) show the logical error rate $e_{\rm log}$ for the error rates of SWAP gate $e_{\rm swap}$. (c1, c2, c3) show the trade-off relationships between $p_{\rm log}$ and $e_{\rm log}$ for configuration 1, 2, and 3, respectively. The configurations 1, 2 and 3 represented by $(p_{\mathrm gen}, L, e_{\mathrm init}, d)$ are (0.3, 19, 0.05, 7), (0.1, 33, 0.05, 7) and (0.3, 23, 0.05, 9), respectively.
• Figure 6: The achievable logical error rates are plotted as a function of averaged trial numbers of pre-distillation processes.
• Figure 7: The focus of existing papers and the positioning of our work. Focused points of each paper are written in bold font.