Future quantum networks will rely on control-plane decisions such as routing, scheduling, entanglement provisioning, purification, and memory allocation. Each decision depends on a timely and reliable estimate of the quality of the entanglement that a candidate path can deliver, with end-to-end fidelity as a central metric. Inspired by the optical-networking experience with quality-of-transmission (QoT) estimation, this article asks when a quantum controller should compute fidelity analytically, simulate it, or learn a surrogate model. The optical analogy is useful but incomplete: optical QoT estimation often predicts a scalar transmission margin, whereas quantum QoT estimation must account for probabilistic entanglement generation, random memory waiting times, decoherence, state consumption, and measurement constraints that can make fidelity a stochastic target. We propose a compute/simulate/learn framework for quantum QoT estimation and illustrate it with a simulation-based proof of concept. Our study shows that analytical composition can be sufficient in simple regimes, that simulation becomes necessary when stochastic memory effects shape the delivered fidelity distribution, and that lightweight learned surrogates can approximate simulator labels at much lower runtime cost for online control. We close with open challenges for deployment, including stochastic targets, sim-to-real transfer, data-generation cost, physics-informed learning, and generalization beyond individual paths to full network topologies.
Figures & tables
Fig. 1: Entanglement distribution along a repeater path. Elementary links are generated probabilistically and then fused by Bell-state measurements at intermediate repeaters. The final end-to-end fidelity is affected not only by the elementary-link qualities, but also by swap imperfections and memory decoherence accumulated while neighboring links wait.
Source
Offline cost
Online cost
Accuracy
Parameters needed
Analytical
None
Low
Regime-dependent
Exact, fresh
Simulator
None
High
High
Exact, known
Learned surrogate
High
Low
Training-dependent
Implicit, from data
Offline cost for the surrogate covers data generation and training.
TABLE I: Sources of a Quantum QoT Estimate
Fig. 2: Decision-aware machine-learning workflow for quantum QoT estimation. The upper part shows the offline training workflow: candidate path configurations are evaluated with a quantum-network simulator to produce fidelity labels, build a QoT dataset, and train a machine-learning surrogate. The lower part shows the online decision flow: a fidelity-estimation request is mapped to analytical computation when the formula is valid and its inputs are fresh, detailed simulation when runtime allows, or the trained machine-learning surrogate when repeated simulation is too costly at decision time.
Fig. 3: Learning the expected fidelity. a) Five-fold cross-validated error of six regressors against the per-fold-calibrated formula; tree ensembles cut the error ∼ 5–6 × . b) Learning curve: the surrogate overtakes the formula after ∼ 80 configurations and keeps improving.
Fig. 4: Generalization to unseen path regimes. Leave-one-family-out error over 270 paths (90 per family; train on two of ring/grid/backbone, test on the third) beside pooled-interpolation error; every model beats the formula on each unseen family, and extrapolation is close to interpolation.
Department of Computer Science, Stony Brook University · Department of Computer Science and Center for Quantum Information Science and Engineering, Virginia Tech
Communication Networks Lab, Technical University of Darmstadt · Institute of Communication Technology, Leibniz University Hannover · Quantum Information Group, IMDEA Networks