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Priority-Aware Routing for Quantum Networks:Integrating Coherence-Time Constraints into Scheduling

Sadhgun Ram Dasi, Aswath Babu H

arXiv:2609.38380v1cs.NIquant-ph

TL;DR

Quantum memories lose coherence over time, so routing and congestion-related queue delays can reduce the fidelity of transmitted qubits. This paper integrates priority-aware queue aging and coherence constraints into path selection. Across the tested topologies, its results report load-stable P2 fidelity on ER graphs and higher P2 fidelity and throughput than loss-only routing on BA graphs.

  • Problem

    Quantum routing commonly optimizes hop count or entanglement-generation rate, while congestion-related queue delays can erode fidelity through decoherence.

    Source: A. Motivation and Challenge · p. 1, §I · p. 1

  • Method

    The protocol integrates coherence-time constraints into path selection using a priority-modulated aging model grounded in Weighted Fair Queueing theory.

    Source: A. Priority-Based Aging Model · p. 3, §X · p. 9

  • Results

    On ER graphs, CA P2 fidelity changes by only 0.04 percentage points across a 9× load increase, while on BA graphs it gains 3.37 to 4.16 percentage points over Dijkstra at operational loads.

    Source: 3) Results · p. 6, §X · p. 9

  • Takeaways & Limitations

    The authors conclude that cross-layer coherence modeling is needed for reliable quantum-network operation across structurally diverse deployment scenarios.

    Source: §X · p. 9

    The fidelity decay equation holds exactly only for pure initial states under pure T2 dephasing; mixed states or amplitude damping yield more complex evolution.

    Source: B. Fidelity Decay and Threshold · p. 2

Abstract

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Quantum networks face a fundamental challenge absent in classical networks; finite memory coherence times mean that queuing delay directly degrades information quality, causing decoherence that has no classical analog. Existing routing protocols optimize for hop count or channel fidelity while treating scheduling delays as a secondary concern, leaving fidelity vulnerable to congestion-induced decoherence. We present a coherence-aware routing protocol that integrates decoherence constraints into path selection via a priority-modulated aging model derived analytically from Weighted Fair Queueing theory, where high-priority traffic receives compressed effective queue delay. We build a custom discrete-event simulator verified against NetSquid (across 104 states), and evaluate across two structurally diverse topology classes under identical physical parameters, isolating topology structure as the sole independent variable. In all experiments, our protocol is benchmarked against loss-only Dijkstra routing and FIFO scheduling as baselines. On topologies, P2 traffic achieves 96.08% fidelity under a 9x load increase with only 0.04 percentage point degradation, versus a 13.51 percentage point collapse for the loss-only baseline; P2 tail latency holds stable at 0.055 ms while Dijkstra degrades 5.5x. On Barabasi-Albert scale-free topologies, our protocol delivers a +4.12 percentage point fidelity advantage with 97.8% higher aggregate throughput at operational loads over the baseline, with a clearly characterized hub-saturation boundary at 160k QPS. FIFO scheduling provides negligible priority differentiation on both topology classes, providing strong evidence that coherence-aware routing-not scheduling alone is responsible for the observed QoS gains.

I. INTRODUCTION

Quantum-network routing must account for finite memory coherence, because congestion and scheduling delays reduce fidelity. This paper integrates priority-aware queue aging and decoherence constraints into path selection, building on models of qubit noise and fidelity.

I. INTRODUCTION

  • Quantum-network applications require qubits to traverse lossy channels and finite-storage intermediate nodes, unlike classical networks where buffering need not degrade data.Memory decoherence can reduce fidelity and potentially cause information loss.Source: §I · p. 1

A. Motivation and Challenge

  • Under congestion, queue waiting erodes fidelity, while prior routing approaches typically prioritize hop count or entanglement-generation rate.The paper asks whether routing can account for states that degrade in transit and generalize across structurally diverse topologies.Source: A. Motivation and Challenge · p. 1

II. RELATED WORK

  • Prior work treats priority mainly as a scheduling-layer mechanism or logical label, whereas this paper makes it a path-selection variable.The paper positions its integration of routing and scheduling against prior work that treats them as independent concerns.Source: A. Motivation and Challenge · p. 1, §II · p. 2

A. Contributions

  • The protocol makes predicted queue waiting time and coherence-time constraints part of path selection alongside channel quality.Its priority-modulated aging model is grounded in Weighted Fair Queueing theory,.Source: A. Contributions · p. 2

A. Density Matrix Evolution

  • The paper models dominant memory noise as T2 dephasing and uses the Lindblad master equation to describe density-matrix evolution.For discrete-event simulation, it uses the operator-sum (Kraus) representation,.Source: A. Density Matrix Evolution · p. 2

B. Fidelity Decay and Threshold

The paper specifies fidelity decay under pure dephasing and uses a threshold to assess whether transmission remains useful. It evaluates routing on ER graphs, whose relatively uniform structure provides a baseline for load balancing across paths.

B. Fidelity Decay and Threshold

  • Fidelity is measured against the ideal initial state, and its decay equation holds exactly for pure initial states under pure T2 dephasing.Mixed states and amplitude damping (T1 processes) yield more complex evolution.Source: B. Fidelity Decay and Threshold · p. 2
  • The paper sets a fidelity threshold following established guidelines, above the classical single-qubit teleportation bound of 2/3.Below that bound, quantum transmission offers no advantage over classical communication.Source: B. Fidelity Decay and Threshold · p. 2

1) Erd˝os–R´enyi Random Topology:

  • The ER evaluation uses 30 randomly placed nodes, with connection probability p = 0.30 for dynamic evaluations and p = 0.15 for static graph generation.ER graphs have low degree variance, no hubs, and typically multiple disjoint paths of roughly equal length.Source: 1) Erd˝os–R´enyi Random Topology · p. 3

2) Barab´asi–Albert Scale-Free Topology:

The evaluation includes BA scale-free graphs, where preferential attachment creates a small number of highly connected hubs. The routing model combines queue delay, priority-based aging, and physical link characteristics to account for coherence constraints.

2) Barab´asi–Albert Scale-Free Topology:

  • BA graphs generate a few highly connected hubs through preferential attachment, and shortest paths often traverse those hubs, creating bottlenecks under elevated load.The observed throughput collapse occurs at ≳160,000 QPS; the topology tests whether routing can use hub-avoiding alternatives before detours run out.Source: 2) Barab´asi–Albert Scale-Free Topology · p. 3

IV. PRIORITY-AWARE SYSTEM MODEL

  • The network is modeled as a directed graph whose nodes are quantum repeaters and whose links carry photon-loss probabilities and propagation latencies.Each repeater has finite quantum memory, classical control processors, and photonic interfaces.Source: §IV · p. 3

A. Priority-Based Aging Model

  • The paper maps priority classes to weights 1, 2, and 3 and analytically relates class delay to inverse priority weight under symmetric load.The delay approximation is justified in the heavy-traffic regime; its packetization error is described as negligible when total capacity greatly exceeds mean packet size.Source: A. Priority-Based Aging Model · p. 3
  • The priority-aware aging model uses WFQ-grounded delay compression so high-priority qubits spend less physical time in queue for fidelity calculations.The model treats scheduling as an abstraction independent of the underlying physical mechanism and can accommodate hardware-level coherence protection as a future extension.Source: A. Priority-Based Aging Model · p. 3

B. EWMA Queue Estimation

The protocol estimates queue delay with an EWMA and uses the estimate in a coherence-time bound. It also escalates long-waiting low-priority packets to preserve fairness while retaining priority differentiation.

B. EWMA Queue Estimation

  • An EWMA estimates queue delay from observed delay, using λ = 0.2 as the smoothing factor without explicit classical state exchange between nodes.The estimate is described as low-overhead.Source: B. EWMA Queue Estimation · p. 4

C. Minimum Coherence Time Bound

  • The minimum coherence-time bound relates hop count, propagation delay, mean queue delay, priority, and a required end-to-end fidelity threshold.For the stated stress-regime parameters, the bound is 312 µs for P2 traffic and 623 µs for P0 traffic; setting Tmem = 400 µs leaves P0 vulnerable while P2 remains viable.Source: C. Minimum Coherence Time Bound · p. 4

D. Priority Escalation

  • Low-priority packets that wait 2 × Tmem are promoted to the next tier, maintaining fairness while preserving differentiation.The factor allows approximately one coherence time of normal service before escalation.Source: D. Priority Escalation · p. 4

V. COHERENCE-AWARE ROUTING PROTOCOL

The protocol combines predicted queue delay, coherence constraints, and priority in path selection. Its routing algorithm filters infeasible packets, prevents loops, and chooses the lowest-cost next hop.

A. Composite Cost Function

  • Priority-aware path selection combines spatial link quality with temporal congestion penalties, emphasizing congestion avoidance with α = 0.5 and β = 10.The protocol models queue state, coherence, and priority before selecting a path.Source: A. Composite Cost Function · p. 4, §V · p. 4

B. Routing Algorithm

  • Each node checks estimated fidelity against a threshold, prevents loops using path history, and evaluates next hops by composite cost.Packets below the estimated-fidelity threshold are dropped; otherwise, the lowest-cost eligible next hop is selected.Source: B. Routing Algorithm · p. 4
  • The routing algorithm runs in O(|E| log |V|) time per packet, matching Dijkstra’s complexity with modified edge weights.For the 30-node topology with about 130 edges, the paper estimates roughly 650 operations per packet.Source: B. Routing Algorithm · pp. 4–5

VI. SYSTEM ARCHITECTURE AND IMPLEMENTATION

The simulator separates its event engine, network entities, and routing logic. Its event queue advances the simulation chronologically, while packet state records timing, priority, quantum state, and path history.

VI. SYSTEM ARCHITECTURE AND IMPLEMENTATION

  • The simulator has three layers: a simulation engine, network entity models, and routing logic.Source: §VI · p. 5

A. Simulation Engine

  • A min-heap orders future events by timestamp, and handlers process them chronologically as simulation time advances.Source: A. Simulation Engine · p. 5

1) Quantum Packet:

  • Packet state includes generation time, priority, an evolving density matrix, and path history.Source: 1) Quantum Packet · p. 5

2) Quantum Node:

The network model uses priority-sorted virtual output queues and dynamically estimated queue delays. The evaluation uses a 400 µs memory stress regime, validates its dephasing implementation against NetSquid, and compares ER and BA topologies under matched physical parameter distributions.

2) Quantum Node:

  • Each priority class has a virtual output queue with capacity 10; arrivals to a saturated class are immediately tail-dropped.Source: 2) Quantum Node · p. 5

C. Routing Logic

  • The routing module computes edge weights dynamically using priority-aware aging and EWMA-based queue estimates.Source: C. Routing Logic · p. 5

D. Validation

  • Across 104 randomly sampled quantum states, the simulator’s Kraus dephasing implementation matched NetSquid with MAE < 10^-6.NetSquid served only as a validation oracle; reported simulations were produced by the custom engine.Source: D. Validation · p. 5

VII. EXPERIMENTAL METHODOLOGY AND RESULTS

  • The evaluation comprises three suites: per-priority load sweep, multi-seed robustness validation, and scale-free topology generalization.Source: §VII · p. 5

A. Core Network Parameters

1) Erd˝os-R´enyi (ER) Topology:

2) Barab´asi–Albert (BA) Scale-Free Topology:

C. Traffic Generation

The ER load sweep evaluates fidelity and tail latency across priority classes as offered load increases. CA keeps P2 fidelity and P95 latency nearly unchanged across the sweep, while Dijkstra’s P2 fidelity and latency worsen.

C. Traffic Generation

  • The workload assigns 60% of traffic to P0, 30% to P1, and 10% to P2.The paper describes background QKD as the majority workload and P2 as latency-sensitive traffic.Source: C. Traffic Generation · pp. 5–6

2) Method:

  • The ER sweep runs from 20k to 180k QPS for 1000 ms per load point, with all three protocols using identical topology and workload configurations.Source: 2) Method · p. 6

3) Results:

  • 96.08% to 96.04%: CA P2 fidelity shifts only 0.04 percentage points across a 9× load increase; CA P2 P95 latency stays at 0.055 ms.Dijkstra P2 fidelity falls 13.51 percentage points, from 95.26% to 81.75%, while its P95 latency rises 5.5×, from 0.063 ms to 0.346 ms.Source: Table II · p. 6, 3) Results · p. 6
  • FIFO shows near-identical fidelity across priorities and identical P95 latency, with no measurable QoS differentiation.At 20k QPS, FIFO fidelity is 89.78% for P2 and 89.71% for P0; P95 latency is approximately 0.152 ms.Source: 3) Results · p. 6, Figure 1 · p. 6

1) Objective:

  • The multi-seed robustness objective is tested with 30 simulations across five seeds, three workload levels, and two protocols.Each run lasts 5000 ms.Source: 1) Objective · p. 6, 2) Method · p. 6

3) Results:

On ER graphs, coherence-aware routing preserves P2 fidelity advantages across load levels and keeps low-priority traffic above the utility threshold where Dijkstra falls below it. On BA graphs, it improves fidelity and throughput at operational loads, with hub saturation defining its boundary.

3) Results:

  • 5.31–7.15 percentage points is CA’s P2 fidelity advantage over Dijkstra across ER load levels, growing under congestion.Table III reports mean end-to-end fidelity across five seeds.Source: Table III · p. 6, 3) Results · p. 6
  • 69.57% at 5k QPS and 68.10% at 8k QPS put Dijkstra P0 below Fmin = 0.70; CA reaches 81.46% and 81.01%, respectively.CA’s improvements are 11.89 and 12.91 percentage points at those loads.Source: 3) Results · pp. 6–7, Figure 2 · p. 7
  • On ER, CA’s P2 fidelity varies by only 0.30 percentage points across a 3.2× load increase, with SEM ≤0.03% across conditions.The reported values are 92.42% and 92.12%.Source: 3) Results · p. 7
  • +3.37 to +4.16 percentage points P2 fidelity advantage and 35–61% higher aggregate throughput characterize CA’s BA operational-load results (≤100k QPS).The table covers a full load sweep across all protocols.Source: 3) Results · p. 7, Table IV · p. 7
  • At 160k QPS on BA, CA retains a +0.50% fidelity advantage while delivering 97.8% more packets than loss-only routing.The temporal penalty term routes around congested hubs, trading slightly longer paths for network utilization.Source: 3) Results · p. 7, Table IV · p. 7
  • Beyond 160k QPS on BA, CA fidelity falls to 76.47% at 220k QPS, while Dijkstra maintains 83.84% by dropping more packets.Hub saturation overwhelms EWMA-based queue estimation, marking the operational boundary for CA on this topology.Source: 3) Results · p. 7, Table IV · p. 7
  • CA’s P2 fidelity advantage is larger on ER than BA at equivalent loads, while FIFO’s near-identical priority-class fidelity persists across topologies.The topology comparison attributes the larger ER advantage to greater path diversity; the FIFO finding is reported as topology-independent.Source: Table V · p. 7, 3) Results · p. 7

VIII. DISCUSSION

The discussion links priority-aware path selection to both congestion resilience and topology-dependent performance limits. It also identifies the single-qubit scope and the stress regime used to distinguish priority classes.

A. Operating Mode Transition

  • As Tmem/DW increases, routing shifts from speed toward path diversity when temporal penalty βΨ dominates spatial loss αLuv.DW is the mean waiting time.Source: A. Operating Mode Transition · p. 8

B. Capacity Extension

  • At near-saturation on BA topologies, coherence-aware routing delivers up to 97.8% more packets than loss-only routing by routing around congested hubs.The reported operating point is 160k QPS.Source: B. Capacity Extension · p. 8

C. Fidelity Load Immunity

  • ER P2 fidelity shifts only 0.04 percentage points across a 9× load increase, and the cost function redirects P2 traffic before queues build up.The passage says this supports fidelity SLAs of FP2 ≥96% at loads up to 180k QPS on ER topologies.Source: C. Fidelity Load Immunity · p. 8

D. Why FIFO and Loss-Only Routing Fail

  • FIFO gives negligible priority differentiation, while loss-only Dijkstra ignores queue delay and routes through high-centrality bottlenecks under load.The coherence-aware protocol avoids congested nodes through its temporal penalty term βΨ.Source: D. Why FIFO and Loss-Only Routing Fail · p. 8

E. Topology-Dependent Operational Envelope

  • ER gains grow from +0.82 percentage points at 20k QPS to +12–+14 under congestion, while BA gains are 3–4 points through 160k QPS before hub saturation.The BA load sweep shows fidelity advantage up to 160k QPS before collapse beyond the operational envelope.Source: E. Topology-Dependent Operational… · p. 8, Figure 3 · p. 8

F. On the Stress Regime Choice

  • The Tmem = 400 µs stress regime is viable for P2 traffic, which requires at least 312 µs, but below the 623 µs stated for comfortable P0 operation.The passage describes this choice as deliberately stressing low-priority traffic while keeping P2 viable.Source: F. On the Stress Regime Choice · p. 8

A. Single-Qubit Scope

  • The evaluation models individual-qubit transmission rather than entanglement distribution; Bell-pair routing would add per-qubit aging and a swap-success penalty.The passage identifies calibration of γ relative to α and β, and handling swap failures that strand half-pairs, as open questions.Source: A. Single-Qubit Scope · pp. 8–9

B. Markovian Noise Assumption

The discussion identifies modeling and adaptation boundaries, including Markovian noise, EWMA lag, fixed weights, and omitted hardware-protection overhead. The conclusion reports load-stable ER performance and a bounded operating envelope on BA topologies.

B. Markovian Noise Assumption

  • The decoherence model assumes memoryless environmental interactions; non-Markovian behavior in some NV and solid-state memories would require more complex fidelity evolution and numerical integration.The passage identifies this as a physical-accuracy limitation for those platforms.Source: B. Markovian Noise Assumption · p. 9

C. EWMA Lag and Hub-Aware Queue Estimation

  • EWMA queue-estimation lag is amplified at BA hubs, collapsing the operational envelope beyond 160k QPS; degree-weighted λ is proposed as a mitigation.The proposed weighting increases update responsiveness with node centrality.Source: C. EWMA Lag and Hub-Aware Queue… · p. 9

D. Fixed Parameters and Adaptive Optimization

  • The experiment holds α and β constant despite changing loads, topologies, and hardware conditions; adaptive optimization is proposed as future work.The passage suggests formulating parameter adaptation as reinforcement learning with delivered P2 fidelity as the reward signal.Source: D. Fixed Parameters and Adaptive… · p. 9

E. Hardware-Aware Protection Modeling

  • Explicitly modeling dynamical-decoupling gate-error and energy costs is identified as a step toward physically concrete priority-based hardware allocation.The passage frames this as moving the aging model from a scheduling abstraction toward a full physical implementation.Source: E. Hardware-Aware Protection Modeling · p. 9

X. CONCLUSION

  • The protocol integrates coherence-time constraints into path selection and uses a WFQ-grounded priority-modulated aging model for coherence-aware path-cost computation.The passage cites Proposition 1 as the theoretical grounding.Source: §X · p. 9
  • ER P2 fidelity varies by only 0.04 percentage points versus a 13.51-point Dijkstra collapse; BA coherence-aware routing gains 3.37–4.16 points and up to 97.8% throughput.The reported BA operational envelope extends to 160k QPS; FIFO provides negligible priority differentiation on both topology classes.Source: §X · p. 9
  • Loss-only routing causes P0 fidelity to fall below the Fmin = 0.70 threshold under moderate load, alongside a topology-dependent operational envelope.The passage says this underscores the necessity of cross-layer coherence modeling for reliable operation across structurally diverse deployment scenarios.Source: §X · p. 9
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