Feasibility of Logical Bell State Generation in Memory Assisted Quantum Networks

TL;DR

This paper assesses the practicality of generating and storing logical Bell states in quantum networks using error correction, simulating protocols with realistic parameters to identify error thresholds and performance limits.

Contribution

It introduces two lattice surgery-based protocols for logical Bell state generation in quantum networks and evaluates their performance with realistic experimental noise models.

Findings

Logical error thresholds are around 10^{-3} for small codes.

Hardware improvements are necessary for advantageous logical Bell state protocols.

Non-local protocol rates reach up to 32.53 Hz over 1-80 km distances.

Abstract

This study explores the feasibility of utilizing quantum error correction (QEC) to generate and store logical Bell states in heralded quantum entanglement protocols, crucial for quantum repeater networks. Two lattice surgery-based protocols (local and non-local) are introduced to establish logical Bell states between distant nodes using an intermediary node. We simulate the protocols using realistic experimental parameters, including ion trap memories, noisy optical channels, frequency conversion, and non-destructive detection of photonic qubits. The study evaluates rotated and planar surface codes alongside Bacon-Shor codes for small code distances ($d = 3, 5$) under depolarizing and physical noise models. Pseudo-thresholds are identified, with physical error rates above $p_{\text{err}} \sim 10^{-3}$ offering no advantage over unencoded Bell states under depolarizing noise. Pseudo-thresholds are also reevaluated in terms of gate error rates $p_{\text{err}_H}$, $p_{\text{err}_{CX}}$, and $p_{\text{err}_M}$. For a distance of 1 km between the end node and the intermediary, an advantage over unencoded Bell-state heralded protocols requires reducing gate error rates by an order of magnitude ($0.1p_{\text{err}_H}$, $0.1p_{\text{err}_{CX}}$, and $0.1p_{\text{err}_M}$). These results highlight the need for significant hardware improvements to implement logical Bell state protocols with quantum memories. Additionally, the non-local protocol rate was analyzed, achieving rates up to $(32.53 \pm 1.53) \, \mathrm{Hz}$ over distances of $1$ to $80 \, \mathrm{km}$ between the end node and the intermediary node.