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A Link Layer Protocol for Quantum Networks

Axel Dahlberg, Matthew Skrzypczyk, Tim Coopmans, Leon Wubben, Filip Rozpędek, Matteo Pompili, Arian Stolk, Przemysław Pawełczak, Robert Knegjens, Julio de Oliveira Filho, Ronald Hanson, Stephanie Wehner

arXiv:1903.09778v1quant-ph

TL;DR

Existing quantum networks lack a hardware-connected stack and link-layer protocols for turning heralded entanglement experiments into a robust service. This paper defines a functional stack, builds physical and link-layer protocols around near-term hardware, and evaluates them through simulation and hardware validation. The protocols remain stable under exaggerated classical-control losses, while the study examines performance tradeoffs and scheduling strategies.

  • Problem

    Existing quantum networks lacked a connected stack and link-layer protocols for producing entanglement as a well-defined service, limiting system-level development.

  • Method

    The paper proposes a functional quantum-network stack, designs platform-independent link-layer protocols informed by NV hardware, and evaluates implemented protocols with simulation and hardware data.

  • Results

    The protocols remain stable under exaggerated classical-control-message losses, and the study evaluates more than 169 scenarios spanning throughput, entanglement quality, and scheduling strategies.

  • Takeaways & Limitations

    The link layer can provide a robust entanglement service without requiring higher layers to know detailed device physics, while future network-layer control will require smart scheduling.

  • Takeaways & Limitations

    The protocol does not eliminate all distributed-state inconsistencies from lost classical control messages and uses limited two-way recovery because such losses are expected to be rare.

Abstract

from arXiv · show

Quantum communication brings radically new capabilities that are provably impossible to attain in any classical network. Here, we take the first step from a physics experiment to a fully fledged quantum internet system. We propose a functional allocation of a quantum network stack and construct the first physical and link layer protocols that turn ad-hoc physics experiments producing heralded entanglement between quantum processors into a well-defined and robust service. This lays the groundwork for designing and implementing scalable control and application protocols in platform-independent software. To design our protocol, we identify use cases, as well as fundamental and technological design considerations of quantum network hardware, illustrated by considering the state-of-the-art quantum processor platform available to us (Nitrogen-Vacancy (NV) centers in diamond). Using a purpose built discrete-event simulator for quantum networks, we examine the robustness and performance of our protocol using extensive simulations on a super-computing cluster. We perform a full implementation of our protocol, where we successfully validate the physical simulation model against data gathered from the NV hardware. We first observe that our protocol is robust even in a regime of exaggerated losses of classical control messages with only little impact on the performance of the system.We proceed to study the performance of our protocols for 169 distinct simulation scenarios, including tradeoffs between traditional performance metrics such as throughput and the quality of entanglement. Finally, we initiate the study of quantum network scheduling strategies to optimize protocol performance for different use cases.

1 INTRODUCTION

Quantum networks require new architectures because qubits cannot be copied, while entanglement enables long-distance communication and applications beyond classical networks. The paper proposes a functional stack and physical/link-layer protocols, then evaluates them through simulation and hardware validation.

  • Motivation: Qubits cannot be copied, ruling out signal amplification or repetition to overcome transmission losses across great distances.Entanglement provides a basis for quantum repeaters and long-distance communication.
  • Motivation: Heralded entanglement generation confirms whether an entanglement attempt succeeded, supporting efficient long-distance quantum communication.The confirmation signal is needed because entanglement generation is probabilistic.
  • Contributions: The paper identifies systematic use cases and design considerations from entanglement properties and near-term quantum-hardware limitations to guide its stack and protocols.The NV platform illustrates the technological considerations.
  • Contributions: The proposed stack assigns the link layer responsibility for producing entanglement between neighboring nodes sharing a direct physical connection.The physical layer contains hardware and connections that support synchronized heralded-entanglement attempts.
  • Contributions: The paper constructs physical and link-layer protocols that convert ad-hoc heralded-entanglement experiments into a well-defined service, with a platform-independent link-layer design.The physical implementation focuses primarily on NV hardware but is intended to transfer to other platforms with adaptations.
  • Evaluation: The protocols are implemented and evaluated with a discrete-event simulator across more than 169 scenarios, including throughput, latency, entanglement fidelity, and scheduling strategies.The study includes short- and long-distance NV-based scenarios and compares simulation with real hardware data.

2 RELATED WORK

Prior work addressed parts of quantum networking, including repeater stacks, distillation, trusted QKD networks, and software-defined control, but did not provide a complete hardware-connected stack with concrete protocols for end-to-end quantum communication.

  • Quantum-network proposals: Earlier proposals outlined functional allocations for quantum repeaters and entanglement distillation but provided neither concrete control protocols nor hardware connections.Those proposals are complementary to this work.
  • Trusted repeater networks: Trusted-repeater software supports point-to-point QKD applications but does not enable end-to-end qubit transmission or entanglement generation.These systems rely on intermediary nodes that can eavesdrop on the communication.
  • Classical networking: Classical networking contributes ideas such as scheduling, but quantum entanglement properties and hardware constraints require new protocols and network-control methods.The paper distinguishes reusable classical ideas from quantum-specific requirements.
  • Research gap: The authors report no prior system-level paper proposing a quantum network stack with protocols for concrete hardware implementations.This gap motivates the paper’s protocol and hardware integration work.

3 DESIGN CONSIDERATIONS FOR QUANTUM NETWORK ARCHITECTURES

The paper organizes quantum-network architecture around entanglement’s properties, near-term hardware constraints, and application requirements. It proposes a layered stack in which physical devices attempt entanglement and higher layers coordinate robust, application-independent services.

  • Fundamental considerations: Entanglement enables teleportation and long-distance links through swapping, but it must be coordinated with classical control information.Teleportation consumes an entangled link, while swapping can connect shorter links into longer chains.
  • Fundamental considerations: Heralding confirms whether an entanglement attempt succeeded, allowing nodes to use successful links without creating entanglement across many qubits.The heralding signal reports success or failure after the photons are measured at the intermediate station.
  • Technological considerations: Quantum nodes are classified as controllable nodes, which store qubits and perform decisions, or automated nodes, which execute preprogrammed timing-controlled operations.Controllable nodes can act as repeaters, routers, or application end nodes; automated nodes can support entanglement swapping along a chain.
  • Use cases: The architecture targets four use cases: network-layer long-distance entanglement, Measure Directly, Create and Keep, and Send Qubit.These use cases differ in whether entanglement is stored, measured immediately, or used for teleportation.
  • Network stack: The proposed physical layer contains hardware and synchronization mechanisms, while the link layer converts repeated physical attempts into a robust entanglement-generation service.The link layer fulfills requests or returns a timeout; the network layer can use it to create longer-distance entanglement through swapping.

4 LINK LAYER DESIGN CONSIDERATIONS

The link layer exposes a platform-independent entanglement service through parameterized requests and structured responses. Its design accounts for fidelity, throughput, latency, memory constraints, physical generation procedures, and failure recovery.

  • 4.1 Desired Service: The link layer offers robust entanglement creation between controllable nodes over links that may include automated nodes, abstracting hardware-specific capabilities into high-level parameters.Higher layers request entanglement without depending on the underlying hardware platform.
  • 4.1.1 Requesting entanglement: CREATE requests specify operational requirements including remote node, request type, batching, atomicity, completion signaling, timeout, purpose, and minimum fidelity.Create-and-keep and create-and-measure requests support different storage and throughput needs.
  • 4.1.1 Requesting entanglement: Fidelity F measures entanglement quality, with F = 1 as the ideal target and F ≥1/2 often desirable; higher fidelity can require more preparation time.The protocol therefore permits different Fmin values rather than fixing one per hardware platform.
  • 4.1.2 Response to entanglement requests: Responses can identify the entangled pair, local memory qubit, estimated goodness, measurement outcome, creation time, and time when goodness was established.For create-and-keep requests, goodness G estimates fidelity and should satisfy G ≥Fmin.
  • 4.1.2 Response to entanglement requests: The protocol reports timeout, unsupported fidelity, insufficient memory, remote refusal, and expiration as explicit failure or recovery conditions.Permanent and temporary storage shortages are distinguished for atomic requests.
  • 4.4 Physical Entanglement Generation: Performance is evaluated using throughput and multiple latency measures, including per request, per pair, and scaled latency.The physical procedure synchronizes photon generation and heralding between nodes A and B through an intermediate station H.
  • 4.4 Physical Entanglement Generation: The NV platform exposes a fidelity-rate tradeoff: F ≈1 −α and psucc ≈2αpdet, with pdet ≪1.The parameter α controls the preparation tradeoff while the communication qubit emits a photon after a 5.5µs sequence.

5 PROTOCOLS

The protocols allocate physical-layer midpoint heralding and link-layer entanglement management into coordinated services. The MHP performs tightly timed generation attempts, while the EGP manages requests, hardware resources, fidelity estimates, scheduling, and replies.

  • Protocol architecture: The EGP uses the MHP to turn heralded entanglement generation into a defined link-layer service with authenticated, reliable classical communication.The MHP is designed for direct implementation over physical heralded-entanglement hardware, while the EGP satisfies link-layer service requirements.
  • Physical Layer MHP: The MHP polls the EGP at each timestep, remains stateless, and triggers generation only when the higher layer supplies a “yes” response and parameters.A batched operation can reduce polling overhead when the polling delay exceeds the minimum MHP generation cycle.
  • Physical Layer MHP: Timestamped attempt IDs let the midpoint match GEN messages to detection windows, verify matching IDs and detection counts, and return success, failure, or the produced Bell state.The EGP uses returned IDs to match replies to outstanding requests and update pair counts.
  • Link Layer EGP: The EGP coordinates CREATE requests through synchronized distributed queues, three use-case priorities, qubit management, fidelity estimation, and deterministic scheduling.The fidelity estimation unit supplies parameters such as α and an estimated minimum completion time; requests exceeding tmax are rejected.
  • Link Layer EGP: The EGP rechecks hardware parameters before issuing MHP instructions, encodes request and progress information in IDs, and propagates successful replies with estimated entanglement quality.The scheduler obtains a current α value, while the FEU supplies the Goodness reported upward after successful attempts.
  • Protocol operation and recovery: Emission multiplexing can increase throughput for the MD use case, but classical-message losses can create distributed-queue inconsistencies handled through later EXPIRE messages.The protocol avoids additional two-way discussion because such losses are expected to be extremely rare.

6 EVALUATION

The evaluation uses a fully implemented simulator across 169 scenarios, validated against NV hardware, to assess robustness, performance trade-offs, and scheduling strategies. Results show resilience to exaggerated classical-message losses, workload- and fidelity-dependent performance, and latency trade-offs under scheduling.

  • Evaluation design: 169 simulation scenarios evaluate three request types across Lab and QL2020 hardware models, including long robustness runs and short trade-off and scheduling runs.The simulator models quantum hardware and communication links, while the physical model is validated against the realized Lab setup.
  • Robustness: Loss probabilities up to 10^-4 leave stable execution with maximum relative differences of 0.005 in fidelity, 0.027 in throughput, and 0.629 in latency.The recovery mechanisms prevent EXPIRE messages in the reported runs; the latency difference may reflect failure to reach steady state.
  • Performance trade-offs: Higher target fidelity lowers attempt success probability and directly scales throughput, while higher incoming request frequency increases scaled latency through queue growth.The fidelity trade-off is measured in QL2020 with kmax = 3 and fP = 0.99; higher Fmin is not satisfiable for NL in the reported sweep.
  • Performance metrics: 6.05 < thavg < 6.47 NL/CK and 6.51 < thavg < 7.09 MD in high- and ultra-load Lab scenarios, with MD higher because it avoids memory-qubit initialization.For QL2020, NL/CK throughput is about 14 times lower because each attempt waits 145 µs for a reply from H.
  • Scheduling: 10.3 s with FCFS and 3.5 s with WFQ is the average scaled latency for NL, while MD latency increases under WFQ by factors of 2.49 and 1.28.The comparison covers uniform and no-NL-more-MD request patterns; throughput is less affected, with a maximal FCFS–WFQ difference of factor 1.16.

7 CONCLUSION

The conclusion positions the work as a step toward large-scale quantum networks by combining design requirements with protocols grounded in actual quantum hardware. It presents the link layer as a robust service and identifies scheduling as an important future challenge.

  • 7 CONCLUSION: The work combines a top-down inventory of design requirements with a bottom-up approach based on actual quantum hardware.The authors frame this combination as advancing quantum networks toward large-scale realization.
  • 7 CONCLUSION: The link layer can provide a robust entanglement service without requiring higher layers to know detailed device physics.The conclusion identifies a robust network-layer control protocol as the next step.
  • 7 CONCLUSION: At the network layer, and with larger quantum memories, scheduling may be needed to address memory lifetimes and coordinate actions across nodes.The authors identify this as requiring substantial computer science and engineering effort.

A.2 Entangled states

Entangled states cannot be factorized into separate qubit states, producing quantum correlations between distant qubits. Bell states form a useful family whose correlations and local-gate transformations support heralded entanglement generation.

  • Entangled states cannot be factorized into individual qubit states and therefore exhibit genuinely quantum correlations between nodes.
  • The Bell state |Φ+⟩ is a superposition of both qubits being |0⟩ and both being |1⟩.
  • Bell-state measurement outcomes in X, Z, and Y bases are perfectly correlated or anti-correlated depending on the state.
  • Local bit- and phase-flip gates on one qubit can transform any Bell state into another.
  • Heralded generation returns either failure or one of |Ψ+⟩ and |Ψ−⟩, which can be interconverted by applying a Z-gate to one qubit.
  • Fidelity quantifies closeness to an ideal target state, while repeated measurements and QBER estimates are used to assess noisy entangled states.

A.4 Decoherence

Quantum-memory noise increases with storage time and is characterized by coherence-related timescales. The section illustrates fidelity decay for entanglement stored in NV electron states as communication distance increases.

  • Quantum-memory noise depends on how long a qubit remains stored and is characterized by T1, T2, and T2* timescales.
  • An NV entangled state stored in electron states with T2 = 1.46 s loses fidelity as the communication time, represented by fiber distance, increases.

B TESTING

The testing protocol estimates entanglement quality from measurement errors and extends full-state testing by interspersing random test rounds. Test-round QBER supports confidence about untested data rounds, while correlated noise and quantum checksums constrain the approach.

  • Standard testing procedure: Fidelity cannot be measured from one state copy, so repeated measurements in X, Z, and Y bases estimate QBER and thereby fidelity.
  • Limitations: Quantum CRCs are theoretically possible but technologically infeasible for many years, while application-level error correction can make fast test rounds preferable.
  • Limitations: The protocol assumes identical independent states and consumes all entangled pairs during testing, leaving correlated noise and unmeasured-pair inference as unresolved challenges.
  • Sampling protocol: The extended protocol randomly selects test rounds and measurement bases over a sampling window, recording outcomes and estimating QBER across tested and untested rounds.
  • Sampling protocol: With confidence determined by N and q, QBER from test rounds estimates QBER for untested data rounds and informs their average fidelity.
  • Simulation support: NetSquid provides a discrete-event framework for simulating quantum information transmission, memory decay, and stochastic communication protocols.

C.1 Validation of simulation

The simulation model is compared with NV hardware measurements in a laboratory scenario. The comparison evaluates measurement correlations, inferred fidelities, and single-attempt generation success probabilities.

  • The validation scenario applies a fixed Z-axis rotation at node A, followed by matched-basis measurements at nodes A and B.
  • Measurement correlations are computed from the joint outcomes mA and mB in the agreed X, Y, or Z basis.
  • Fidelity relative to the heralded target state |Ψ±⟩ is expressed as a function of the measured correlations.
  • The analysis assumes independence between rounds when propagating standard deviations.
  • The laboratory simulation and NV hardware data show good agreement across the reported validation measures.

C.2 Simulation data

The simulations evaluate mixed-priority request handling across multiple scheduling strategies, focusing on latency and throughput over time. Across the examined scenarios, scheduler choice has little effect on throughput, while latency patterns depend on queueing and request size.

  • Simulation design: 1618 simulation runs covered 169 long-run scenarios plus shorter runs varying request load and minimum requested fidelity.The long runs comprised 2 × 169 runs with 120 hours of wall time each; shorter runs comprised 1280 runs with 24 hours each.
  • Simulation design: Five usage patterns varied request load and the maximum number of requested pairs using a probability based on success probability and expected attempt cycles.The request-generation probability is f · psucc/(E · k), with E differing between Lab request types.
  • Scheduling strategies: FCFS strongly correlates request latencies across request types because all requests share one queue.Scaled latency, particularly for MD, can diverge because requests contain different numbers of pairs.
  • Results: Scheduler type has relatively little effect on throughput in the simulated mixed-request scenarios.Figures 17–22 plot throughput over simulated time, while Tables 3 and 4 collect average throughput and latency metrics.

D.1 The simulated network

The simulated network represents quantum processors, optical and classical links, heralding, noise, gate operations, and memory behavior as modular components. Its NV-based parameters capture operation durations, decoherence, entanglement-generation success, and hardware-specific parallelism constraints.

  • Network components: The simulator implements the physical and link-layer protocols on modular simulated quantum hardware and can be configured for other hardware platforms.The model includes quantum-processing devices, fiber and classical connections, and heralding stations.
  • Network components: Quantum-processing devices model communication and memory qubits, gate operations, entanglement triggers, readout, and associated noise and timing.Memory decoherence, gate noise, probabilistic photon-mediated entanglement, and measurement delays are represented explicitly.
  • NV platform: NV-platform behavior is determined by operation durations, coherence times, noise levels, and the physical structure of electron and carbon-spin qubits.The simulation uses parameters for the Lab configuration and records experimentally realized values separately.
  • NV platform: Carbon-spin pulse sequences provide rotations and dynamical decoupling but impose limits on parallel operations involving carbon and electron spins.The simulator includes microwave-pulse gates, waiting-time rotations, initialization, swapping, and gate-noise models.

D.6.1 Optical Link Error Model.

The optical-link model uses conservative worst-case Gigabit Ethernet parameters to estimate transmission errors. Under the modeled assumptions, 15 km and 20 km links show no frame errors, while errors begin beyond 40 km with a sharp transition to disconnection.

  • Optical link assumptions: The model assumes 0.5 dB/km attenuation, connector and splice losses, a 3 dB safety margin, −1 dBm transmission power, and −24 dB receiver sensitivity.It models IEEE 802.3 frame errors rather than only abstract link loss.
  • Frame-error behavior: 15 km and 20 km links have perfect frame-error probability under zero-splice assumptions.These distances correspond to the two example long-distance Quantum Internet topologies.
  • Frame-error behavior: Frame errors appear only beyond 40 km, followed by a narrow transition from no errors to a disconnected interface.The modeled frame-error rate transitions sharply to one.
  • CRC analysis: The CRC model separately estimates the probability that a frame error remains undetected by mapping distance to SNR and then to BER.This extends the link model beyond whether errors occur to whether CRC detects them.

D.6.2 Optical Link CRC Error Model.

This section describes the distributed queue machinery used to track entanglement requests and maintain consistent ordering between controllable nodes. Requests are assigned to priority queues with bounded capacity and queue identifiers that preserve ordering properties.

  • Distributed queue: The Distributed Queue Protocol stores CREATE-request parameters and metadata such as creation time, minimum time, and MHP timeout cycle.It tracks which application each entangled qubit belongs to across peer nodes.
  • Queue organization: Priority requirements are implemented by assigning requests to multiple queues selected by the scheduler.The total number of queues is denoted by L.
  • Queue organization: Each queue holds at most x entanglement requests, each with associated metadata and an absolute queue ID.The queue ID is a tuple identifying the designated queue and the request’s position.
  • Ordering guarantees: Queue identifiers impose total ordering and ensure earlier requests on the same queue receive lower queue positions.The ordering is defined using request arrival times and modular queue indices.
  • Ordering guarantees: The protocol’s core objective is for both nodes to agree on the items and ordering of their shared queues.Each controllable end node maintains a local queue representation.

E.1.2 DQP Queue Establishment.

The DQP establishes a synchronized distributed queue for entanglement requests between two nodes, preserving shared identifiers, consistency, uniqueness, and fairness. It uses message-based acknowledgment, rejection, retransmission, and timeout handling before requests reach the MHP.

  • Queue properties: The DQP synchronizes entanglement-create requests between two nodes by assigning matching absolute queue IDs.Requests added at either node are eventually represented at both nodes with the same queue identifier.
  • Queue properties: Queue placement guarantees unique identifiers, consistency between replicas, and fair access for continuously issuing nodes.Fair ordering is bounded by the respective window sizes WA and WB.
  • Message exchange: ADD requests are accepted with ACK, rejected with REJ, or removed after timeout when no response arrives.The DQP retransmits lost ADD, ACK, and REJ messages to recover from message loss.
  • Message exchange: DQP packet fields identify the frame, communication sequence, queue, request order, earliest execution cycle, and timeout cycle.The packet format includes OPT, FT, CSEQ, QID, QSEQ, Schedule Cycle, and Timeout fields.
  • MHP operation: The MHP polls the EGP, instructs hardware through pulse sequences, emits photons when requested, and reports heralding outcomes or errors.The midpoint checks timing and queue identifiers before performing the quantum swap and returning a REPLY.

E.3.2 EGP Sequence Diagrams.

The EGP sequence diagrams describe how nodes coordinate entanglement requests, memory availability, expiration, and error recovery. Packet formats define the control information exchanged between the EGP, MHP, and higher layers.

  • Memory and expiration: Memory advertisement exchanges let both nodes verify available communication and storage resources before attempting photon emission.Both nodes must be able to emit photons for the protocol to operate properly.
  • Error recovery: Lost EXPIRE, ACK, REQ(E), or corresponding acknowledgment messages trigger retransmission to prevent deadlock and maintain synchronized resource information.The protocol retransmits expiration and memory-request messages when delivery is uncertain.
  • Error recovery: A lost GEN message produces a NO_CLASSICAL_OTHER reply, prevents an entanglement attempt, and leaves the midpoint sequence number unchanged.The midpoint handles the case where only one end node’s GEN message arrives.
  • Memory and expiration: EXPIRE and ACK exchanges revoke or confirm expired entanglement requests when sequence information shows that nodes are out of sync.An EXPIRE carries sequence information used to revoke stale OK messages at the peer.
  • Packet formats: EGP packet formats encode create parameters, expiration identifiers, memory availability, photon-generation commands, measurement outcomes, success records, and errors.The formats span CREATE, EXPIRE, ACK, REQ(E), POLLEGP, MHP replies, OK, and ERR messages.
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