Optimal Calibration of Quantum Network Links

The gist The reliable distribution of entanglement is essential for the effective operation of quantum networks, and this work develops an analytically derived protocol for optimally assigning activation periods to each link in linear quantum repeater chains subject to fidelity constraints, extending this to general networks with a heuristic approach.

Calibration Modeling

The paper models calibration as a trade-off between link quality and availability, where every link alternates between an activation period and a calibration period The average transmitted fidelity falls from ≈ 1 to ≈ 0.5 over ∼ 10,000 s (∼166 min), after which a ∼2 min calibration restores the link This duty-cycling directly reduces end-to-end throughput and crucially interacts with multi-path orchestration when links are shared among paths. The throughput of USPC is given by Tuspc = A p / (x Ts) / (x Ts + τc).

Constraints on Fidelity and Log-fidelity Variable Spaces

The paper establishes constraints on the activation period ae based on initial fidelity thresholds and end-to-end fidelity requirements Lemma 2 gives the upper bound on the activation period of the link e, ae ≤ 1 / Γ ln (F M e − 1 / 4) Fth e − 1 / 4. The paper then defines a relationship between linear and log-fidelity variable spaces, where Le = ln A / (F M e − 1/4).

Optimal Calibration in Linear Quantum Chains

The optimal allocation for a linear quantum chain is derived analytically through the Quantum Link Orchestration (QLO) Theorem Theorem 3 shows that the throughput T of the quantum network is maximised by allocating links Li as follows: 1) For Lth i ≤ Ωπ: Li = Lth i, 2) For Ωπ < Lth i: Li = Ωπ, and 3) for links above Ωπ, a recursive update rule is used to redistribute the end-to-end budget. The algorithm runs in O(N 2) time.

Calibration-Aware Orchestration in General Networks

For general networks with multiple source–destination paths P, the problem becomes a non-convex program where a single physical activation period is enforced per link The objective function T = X π C π / Y e∈π Le / (Le + K) is neither separable nor jointly concave, necessitating heuristics. Two feasible strategies are proposed: 1) Minimum selection rule (MIN), which assigns Le = min π∈Πe Lπ,e for shared links and Lπ,e for exclusive links, and 2) Greedy Quantum Link Orchestration (GRO), which extends MIN by redistributing the freed calibration budget over exclusive links sorted by descending available headroom.

Simulation Results and Performance Evaluation

Simulations on grid networks confirmed the theoretical ordering T REF ≥ T QLO ≥ T NUM ≥ T GRO ≥ T MIN The gap between QLO and NUM represents the cost of shared-link coordination, which becomes substantial at large n. GRO is shown to weakly dominate MIN with strict improvement whenever freed budget and positive headroom coexist.

Conclusion

The work derives the optimal allocation analytically for linear chains using QLO and establishes a feasible O(M) benchmark (MIN) and an improved heuristic (GRO) for general networks, demonstrating that GRO tracks the numerically optimal solution (NUM) with significant improvement in budget recovery at large network sizes. The ordering T REF ≥ T QLO ≥ T NUM ≥ T GRO ≥ T MIN is confirmed by simulations.

How it works

The paper develops an analytically derived protocol for optimally assigning activation periods to each link in linear quantum repeater chains subject to fidelity constraints, extending this to general networks with a heuristic approach. The process involves formulating calibration-aware entanglement distribution as a network optimisation problem and making contributions such as analytically deriving the optimal calibration schedule for linear quantum network chains, termed Quantum Link Orchestration (QLO).

The QLO Theorem provides a closed-form partitioning rule where links whose per-link fidelity threshold falls below the path-optimal point Ωπ are operated at their individual threshold, and links above Ωπ are clamped to a recursively updated optimal point that redistributes the remaining end-to-end budget. This algorithm runs in O(N 2) time.

In general networks, the paper establishes the minimum selection rule (MIN), which assigns Le = min π∈Πe Lπ,e for shared links and Lπ,e for exclusive links, serving as a feasible O(M) benchmark. Building on this, GRO proposes a heuristic that extends MIN by redistributing the freed calibration budget over each path’s exclusive links sorted by descending available headroom. This heuristic runs in O(P · N 2π + M log M) and weakly dominates MIN with strict improvement whenever freed budget and positive headroom coexist.

The simulation results confirm the ordering T REF ≥ T QLO ≥ T NUM ≥ T GRO ≥ T MIN. REF is an infeasible upper bound since it ignores the end-to-end constraint, while NUM, being feasible, lower-bounds the true optimum; together they bracket it.

The paper addresses calibration by modeling the duty-cycle structure explicitly at the network layer and formulating throughput optimisation as a constrained allocation problem over activation periods The analysis is performed primarily in L-space, where ln Tπ = ln C + P e∈π ln Le / (Le + K). The optimal point ΩL is found by minimizing the Euclidean distance to the optimal point P=(ΩL, ΩL) on a family of hyperboloids.

The final conclusion is that GRO closely tracks the numerically optimal solution (NUM) in small networks, while its ability to recover budget makes it a practical alternative to NUM for deployable strategies. The work addresses several open directions, including relaxing assumptions on fixed paths and incorporating stretched-exponential fits for better accuracy.

How it works

The paper models calibration as a trade-off between link quality and availability, where every link alternates between an activation period and a calibration period The average transmitted fidelity falls from ≈ 1 to ≈ 0.5 over ∼ 10,000 s (∼166 min), after which a ∼2 min calibration restores the link.

The throughput of USPC is given by Tuspc = A p / (x Ts) / (x Ts + τc).

Simulation Results and Performance Evaluation

Simulations on grid networks confirmed the theoretical ordering T REF ≥ T QLO ≥ T NUM ≥ T GRO ≥ T MIN. REF is an infeasible upper bound since it ignores the end-to-end constraint, while NUM, being feasible, lower-bounds the true optimum; together they bracket it.

1. A calibration-aware entanglement distribution system can be developed that analytically derives the optimal calibration schedule for linear quantum network chains, termed Quantum Link Orchestration (QLO), which balances activation time against calibration downtime to maximise throughput under fidelity constraints.

2. The improved system can optimize resource allocation across multiple paths in general networks by proposing the Greedy quantum link Orchestration (GRO) heuristic, which is shown to be feasible and weakly dominates MIN by redistributing the freed budget on each path over its exclusive (unshared) links.

3. The AI system can perform complex, constrained resource allocation in quantum networks by utilizing the numerical optimizer NUM, which is described as a true constrained optimiser of the general network problem, to find solutions that bracket the true network optimum, ensuring that T GRO ≤ T NUM ≤ T⋆ ≤ T QLO.