An Adaptive Purification Controller for Quantum Networks: Dynamic Protocol Selection and Multipartite Distillation

TL;DR

An Adaptive Purification Controller that autonomously optimizes the entanglement distillation sequence to maximize the goodput, eliminating the "fidelity cliffs" in static protocols and preventing resource wastage in high-noise regimes is proposed.

Abstract

Efficient entanglement distribution is the cornerstone of the Quantum Internet. However, physical link parameters such as photon loss, memory coherence time, and gate error rates fluctuate dynamically, rendering static purification strategies suboptimal. In this paper, we propose an Adaptive Purification Controller (APC) that autonomously optimizes the entanglement distillation sequence to maximize the "goodput," the rate of delivered pairs meeting a strict fidelity threshold. By treating protocol selection as a resource allocation problem, the APC dynamically switches between purification depths and protocol families (e.g., BBPSSW vs. DEJMPS) to navigate the trade-off between generation rate and state quality. Using a dynamic programming planner with Pareto pruning, simulation results demonstrate that our approach eliminates the "fidelity cliffs" inherent in static protocols and prevents resource wastage in high-noise regimes. Furthermore, we extend the controller to heterogeneous scenarios, demonstrating robustness for both multipartite GHZ state generation and continuous variable systems using effective noiseless linear amplification models. We benchmark its computational overhead, confirming real-time feasibility with decision latencies in the millisecond range per link.

Figures (8)

• Figure 1: Goodput optimization with APC on a single hop. Setup: 15 km link, $F_0=0.85$, $T_2=100$ ms, target $F^\star \in [0.84,\,0.92]$. (a) Goodput (pairs per second, log scale) versus $F^\star$ for APC and fixed rounds $r=0,1,2,3$; APC tracks the upper envelope and declares infeasible beyond $F^\star \approx 0.885$. (b) Rounds selected by APC as a function of $F^\star$ (stepwise 0 to 4). (c) Achieved end-to-end fidelity versus target (45$^\circ$ threshold shown); APC meets or slightly exceeds $F^\star$ when feasible while fixed strategies under- or over-shoot.
• Figure 2: APC rounds adapt to gate noise on a 3-hop chain. Setup: total 24 km (3 links), $F_0=0.93$ per link giving $F_{\mathrm{raw}}\approx0.80$ after two swaps, target $F^\star=0.85$, gate or measurement error probability $\varepsilon$ swept from $10^{-4}$ to $3\times10^{-2}$. (a) End-to-end fidelity versus $\varepsilon$ (semi-log in $\varepsilon$) with threshold $F^\star$ marked. (b) Goodput versus $\varepsilon$ (log-log); APC sustains $\sim10^2$ to $5\times10^2$/s until the noise cliff. (c) APC-selected rounds (1 to 4) versus $\varepsilon$, compensating for increasing noise until saturation. (d) At high noise beyond the cliff, additional rounds reduce fidelity because CNOT-induced errors dominate; $r=0$ becomes least bad.
• Figure 3: Operating regime over distance and target fidelity. Setup: 1 hop, $F_0=0.90$, $T_2=80$ ms; distance $5$ to $60$ km and target $F^\star$ in $[0.86,\,0.93]$. (a) Heatmap of $\log_{10}(\text{goodput})$ with gray for infeasible points. (b) APC-selected rounds $r\in[0,6]$ (banded regions show transitions $r=0\to1\to2\ldots$). (c) Achieved fidelity across the same grid; feasible cells meet $F^\star$, with gray indicating failure.
• Figure 4: Memory coherence time $T_2$ induces a feasibility threshold. Setup: 3-hop chain over 24 km total, with per-link $F_0=0.92$ calibrated so that the unpurified end-to-end fidelity is $F_{\mathrm{raw}}\approx 0.77$ as $T_2\rightarrow\infty$. Target $F^\star=0.76$; $T_2$ swept from 1 ms to 1 s. (a) Goodput versus $T_2$ (log--log): below $\sim 9$ ms, decoherence prevents meeting $F^\star$. (b) APC-selected purification rounds versus $T_2$: $r=0$ throughout the viable region, indicating that once memory decay is sufficiently suppressed, swapping alone meets $F^\star$. (c) Achieved end-to-end fidelity versus $T_2$, showing a sharp crossing at the feasibility threshold.
• Figure 5: Protocol/depth adaptation to maximize hard-threshold goodput. Setup: single hop with $F_0=0.85$, distance 15 km, and $T_2=150$ ms. We compare fixed BBPSSW and DEJMPS at $r\in\{1,2\}$ and sweep $F^\star\in[0.84,0.91]$. (a) Goodput versus $F^\star$ (semi-log): APC tracks the upper envelope by adapting depth (and protocol via the selection policy). (b) Achieved fidelity versus target, showing APC meets the constraint while fixed baselines under- or over-shoot. (c) APC-selected rounds versus $F^\star$, exhibiting stepwise increases from $r=0$ up to $r=5$.