SCOPE: A Syndrome-Driven Control Plane for QEC-Enabled Quantum Networks

Abstract: As quantum networks evolve from experimental testbeds to fault-tolerant systems, the primary performance metric shifts from physical link fidelity to end-to-end logical error rate. However, current control planes remain ill-equipped for this transition: routing decisions are typically decoupled from Quantum Error Correction (QEC) strategies, relying on topology or scalar fidelity metrics that fail to predict how specific physical noise structures interact with logical codes. Optimizing this coupled route-and-code performance requires precise, real-time visibility into network error biases, yet traditional active tomography is operationally prohibitive due to throughput collapse and service interruption. We present SCOPE (Syndrome-based COntrol PlanE), a network-layer architecture that enables joint routing and coding optimization using purely passive telemetry. Instead of injecting probes, SCOPE harvests error syndromes -- the parity-check outcomes naturally generated by QEC decoders during user service. By aggregating these signals, SCOPE's inference engine reconstructs the network's time-varying error map, capturing complex, context-dependent noise correlations. This visibility drives a decision engine that proactively pushes optimal route-and-code configurations to source nodes. NetSquid and IBM-calibrated simulations show that SCOPE reduces estimation error by more than 60% relative to a standard EM baseline. In large-scale networks, this precision reduces logical error rates by 30-35% (up to 65%) against topology-aware baselines.

• The paper introduces SCOPE, which uses passive syndrome tomography to construct a dynamic error map for improved network performance.
• It employs a two-stage hybrid model combining differentiable syndrome tomography and deep learning to accurately estimate context-dependent quantum noise.
• SCOPE’s joint routing and code optimization reduces logical error rates by up to 65%, setting a new benchmark for fault-tolerant quantum networking.

A Syndrome-Driven Control Architecture for QEC Quantum Networks

Motivation and Problem Formulation

As quantum networks progress from experimental platforms toward large-scale and fault-tolerant operation, the critical performance benchmark shifts from physical link-level metrics (such as entanglement fidelity) to the end-to-end logical error rate (LER) observed by encoded quantum data. In this regime, the interplay between quantum error correction (QEC) codes and the physical, often bias-dependent, noise processes of the network becomes paramount. State-of-the-art quantum network control planes operate suboptimally in this context, as they either decouple routing from coding or rely on summary scalar metrics that ignore the structure of quantum noise and its interaction with code properties.

Critically, the optimization of LER for real networks with dynamically changing, path- and context-dependent errors requires accurate, real-time visibility into detailed network noise characteristics. Traditional approaches to this—chiefly active tomography—impose prohibitive operational overheads and fail to capture the error landscape during live network service, particularly with resource contention and load-dependent crosstalk. Consequently, existing routing strategies neither exploit nor even observe the underlying error processes relevant to logical transmission fidelity.

SCOPE Architecture: Passive Syndrome-Driven Learning and Optimization

The proposed SCOPE (Syndrome-based COntrol PlanE) system is architected as a logically centralized software-defined control plane for QEC-protected quantum networks. It introduces two core technical contributions:

1. Passive Syndrome Tomography: SCOPE leverages the continuous stream of parity-check syndromes passively generated by QEC decoders as qubits traverse the network. By aggregating these parity measurements from in-flight user traffic, SCOPE reconstructs a dynamic, high-fidelity network error map without halting operation or injecting probes.
2. Joint Routing and Code Optimization: Using this learned error map, SCOPE performs explicit joint optimization over the (route, code) pair for each source-destination transmission, thereby minimizing LER rather than intermediate or proxy metrics.

Tomography Engine

For the error estimation task, SCOPE employs a two-stage hybrid modeling protocol:

• Differentiable Syndrome Tomography (DST): For independent error models, SCOPE formulates the relation between per-edge Pauli noise rates and the global syndrome histogram as a differentiable computational graph. It solves for the optimal per-edge error rates via gradient descent on the Kullback-Leibler divergence between empirically observed and model-predicted syndrome histograms across multiple overlapping paths. This parameter-sharing design enables compositional generalization to unobserved routes.
• Correlation-Aware Deep Learning: For regimes with spatial or temporal error correlations, DST is augmented with deep neural architectures. Specifically, Transformers are used for path-history dependent (sequential) correlations (e.g., coherent errors and memory decoherence), while Graph Neural Networks (GNNs) model structural dependencies (e.g., crosstalk from parallel switching). Adjustments are made over the static DST baseline to yield context-conditional effective error rates, capturing non-Markovian effects.

Decision Engine

The decision engine computes route/code plans that minimize the predicted LER. For independent errors, a code-aware Dijkstra’s algorithm determines optimal paths; when history-dependent errors are significant, context-aware dynamic programming is employed. For teleportation-based networks, interval-based recursive optimization constructs the swap-tree topology which minimizes LER, taking into account waiting-time-induced decoherence and swap operation errors.

SCOPE operates asynchronously and decouples control-plane computation from real-time data-plane circuit-switching, interfacing with classical clusters for routing/code recomputation and pushing precomputed plans to source nodes. This allows microsecond-scale connection setup on-demand with full code/route adaptivity.

Robust Generalization and Adaptation

A distinctive property of SCOPE is its extensibility to operationally realistic scenarios:

• Decoherence and Buffering: Time-dependent memory errors (modeled with T1/T2 timescales) are incorporated via timestamped data and aggregated into the error map.
• Teleportation and Swap Errors: The error mapping function is extended to handle swap-tree-based teleportation, jointly estimating link entanglement, swap operation, and waiting-time errors.
• Heterogeneous Coding: Traffic using multiple QEC codes is supported via a shared physical error map with code-specific syndrome mappings, enabling cross-code transfer learning.
• Incremental Learning: The model is continuously refined using online, incremental updates from new syndrome batches to track non-stationary or drifting noise parameters.
• Network Dynamics: Cold-start and topology changes are handled by initializing new elements with conservative parameters while retaining previous error estimates for unaffected components, ensuring rapid adaptation without global retraining.

Numerical Results and Empirical Evaluation

SCOPE’s efficacy is demonstrated through comprehensive simulation on both idealized networks (NetSquid) and IBM hardware-calibrated noise models:

• Error Estimation Accuracy: In dependent-error regimes, SCOPE’s Transformer/GNN models achieve a 60% reduction in mean absolute percentage error (MAPE) relative to EM baselines, converging to 20% MAPE for link error recovery.
• LER Reduction: Joint route/code optimization enabled by SCOPE reduces logical error rates by 30–35% compared to topology-based routing; under some regimes, improvements reach 65%. The gap between SCOPE and the oracle (ground-truth) strategy is narrow, indicating near-complete observability through passive telemetry.
• Operational Overhead: Full model retraining is completed well within the typical timescale of hardware drift (tens of minutes on commodity hardware for a 100-node network), while online incremental updates require only 1–5 minutes, incurring negligible control-plane communication overhead (sub-25 MB per update at scale).
• Robustness to Model Misspecification: Even with complex, hardware-inherited noise, SCOPE maintains significant accuracy advantages in syndrome distribution prediction (low TVD), although absolute parameter estimation is naturally less precise in these settings.
• Route-Code Ablations: Gains from code-only or route-only optimization are proved to be complementary; full SCOPE (joint optimization) is consistently necessary for maximal LER reduction.

Implications and Prospective Directions

SCOPE establishes a new paradigm for quantum network control grounded in observables relevant to logical transmission fidelity. By exploiting in situ error telemetry, SCOPE provides a foundation for robust, cross-layer optimization in quantum networks subject to nontrivial, context-dependent noise. This approach is practically essential for delivering high-throughput, fault-tolerant QEC-protected services at planetary scale, particularly under the anticipated proliferation of network hardware heterogeneity and dynamic workloads.

Theoretically, SCOPE signals a move away from control architectures rooted in component-level benchmarks or static noise assumptions, favoring instead full-stack optimization driven by observable logical impact. Practically, SCOPE’s architecture is well-aligned with the anticipated trends in quantum network scaling: larger topologies provide more routing path diversity and more syndrome data, and expanded physical capacity supports deployment of larger, bias-tailored QEC codes, amplifying the benefits of dynamic route-code coupling.

Looking forward, the co-design of transport-aware and network-optimized QEC codes, the incorporation of active learning and lifelong adaptation algorithms for evolving noise characteristics, and the integration of SCOPE with next-generation software-defined quantum networking frameworks are promising avenues for further research and systemization.

Conclusion

SCOPE delivers a scalable, syndrome-driven control solution for QEC-enabled quantum networks that unifies passive network telemetry, physics-informed machine learning, and cross-layer route/code optimization. Its ability to continuously adapt to complex, context-dependent network noise yields substantial reductions in logical error rate relative to conventional approaches. SCOPE’s framework is likely to serve as a foundation for robust, adaptive control in future global quantum network deployments and provides a blueprint for leveraging in situ correction data for network-layer optimization.