Nilesh Vyas

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.

Quantum repeaters have promised efficient scaling of quantum networks for over two decades. Despite numerous platforms proclaiming functional repeaters, the realization of large-scale networks remains elusive, indicating that the resources required to do so were thus far underestimated. Here, we investigate the dependence of resource scaling of networks on realistic experimental errors. Using a nested repeater protocol based on the purification protocol by Bennett et. al., we provide an analytical approximation of the polynomial degree of the resources consumed by entanglement routing. Our error model predicts substantially stricter thresholds for efficient network operation than previously suggested, requiring two-qubit gate errors below 1.3% for resource scaling with polynomial degree below 10. The analytical model presented here provides insight into the reason why previous experimental implementations of quantum repeaters failed to scale efficiently and inform the development of truly scalable systems, highlighting the need for high-fidelity local two-qubit gates. We employ our analytical approximation of the scaling exponent as a figure of merit to compare different platforms and find that trapped ions and color centers in diamond currently provide the best route towards large-scale networks.