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NetSquid, a NETwork Simulator for QUantum Information using Discrete events

Tim Coopmans, Robert Knegjens, Axel Dahlberg, David Maier, Loek Nijsten, Julio de Oliveira Filho, Martijn Papendrecht, Julian Rabbie, Filip Rozpędek, Matthew Skrzypczyk, Leon Wubben, Walter de Jong, Damian Podareanu, Ariana Torres-Knoop, David Elkouss, Stephanie Wehner

arXiv:2010.12535v3quant-ph

TL;DR

Quantum-network architectures and protocols can be too detailed for mathematical analysis, creating a need for numerical tools that model physical hardware and time-dependent behavior. The paper introduces NetSquid, a modular discrete-event simulator, and demonstrates its use across quantum switches, repeater chains, atomic-ensemble memories, and large networks. The use cases show that it supports detailed physical and control-plane studies, including switch analysis beyond analytically known regimes and entanglement distribution over chains of up to one thousand nodes.

  • Problem

    Detailed quantum-network architecture proposals are often too complex for mathematical analysis, motivating numerical simulation to determine protocol and hardware requirements.

  • Method

    NetSquid combines discrete-event simulation with quantum-state modelling, modular hardware components, and asynchronous protocol descriptions to simulate quantum networks and modular quantum computing systems.

  • Results

    NetSquid supports use cases spanning quantum-switch control beyond analytical regimes, physical repeater-chain studies, atomic-ensemble memory comparisons, and entanglement distribution over chains of up to one thousand nodes.

  • Takeaways & Limitations

    The platform serves as a design tool for exploring quantum-network protocols, physical hardware choices, and modular architectures under realistic non-idealities.

Abstract

from arXiv · show

In order to bring quantum networks into the real world, we would like to determine the requirements of quantum network protocols including the underlying quantum hardware. Because detailed architecture proposals are generally too complex for mathematical analysis, it is natural to employ numerical simulation. Here we introduce NetSquid, the NETwork Simulator for QUantum Information using Discrete events, a discrete-event based platform for simulating all aspects of quantum networks and modular quantum computing systems, ranging from the physical layer and its control plane up to the application level. We study several use cases to showcase NetSquid's power, including detailed physical layer simulations of repeater chains based on nitrogen vacancy centres in diamond as well as atomic ensembles. We also study the control plane of a quantum switch beyond its analytically known regime, and showcase NetSquid's ability to investigate large networks by simulating entanglement distribution over a chain of up to one thousand nodes.

I. INTRODUCTION

NetSquid addresses the difficulty of analyzing quantum networks with detailed physical behavior and time-dependent control by providing a modular discrete-event simulation platform. It models network hardware and protocols, executes repeated stochastic runs, and supports performance analysis across physical and control layers.

  • Motivation: Quantum-network analysis is difficult because communicating devices create intricate timing dependencies that complicate precise analytical treatment.Detailed physical modelling must also account for time-dependent behavior and the classical control plane orchestrating network devices.
  • NetSquid platform: NetSquid integrates a discrete-event engine, quantum computing library, modular hardware models, and asynchronous protocol programming.The platform is designed to simulate quantum networking and modular computing systems subject to physical non-idealities.
  • Simulation workflow: Simulations model components and physical effects, assign node protocols, and execute many independent runs to estimate network performance statistically.The illustrated repeater-chain use case estimates average output fidelity from repeated stochastic simulations.
  • Quantum modelling: Its component framework represents hardware, communication ports, physical models, and recursively nested subcomponents.The example includes fibre loss and delay, memory decoherence, and quantum-gate error models.
  • Quantum modelling: NetSquid represents quantum information as qubits and supports multiple state representations with trade-offs in versatility, speed, and network scalability.Available representations include ket vectors, density matrices, stabiliser tableaus, and graph states with local Cliffords.
  • Simulation workflow: Discrete-event progression handles control processes and feedback loops while tracking quantum-state decoherence over elapsed time between events.Protocol actions are triggered by events, and new events are generated as the simulation proceeds.

B. Simulating a quantum network switch beyond its analytically known regime

NetSquid reproduces and extends quantum-switch analyses beyond their analytically known regime. It estimates capacity across broader parameter ranges and evaluates state quality under time-dependent memory dephasing.

  • Switch model: The quantum switch distributes Bell pairs and n-partite GHZ states among users connected to a central node by optical links.The switch connects randomly generated Bell pairs using control logic that selects participating users.
  • Beyond analytical analysis: The simulation extends analysis to parameter ranges beyond prior analytical results and to memory dephasing noise beyond the earlier erasure model.The extension covers both broader entanglement-rate estimation and more sophisticated time-dependent noise modelling.
  • Switch protocol: The protocol attempts entanglement generation in parallel, stores successful Bell pairs, and performs an n-partite GHZ measurement after n pairs are available.A finite buffer B limits the memories dedicated to each user link.
  • Capacity analysis: NetSquid reproduces the prior switch model without explicitly constructing its Markov chain and studies a nine-user network’s GHZ-state capacity.Capacity is defined as the number of produced GHZ states per second.
  • State quality: Exponential T2 memory noise is used to evaluate how time-dependent decoherence affects the average fidelity of generated entanglement.This quality analysis complements rate measurements for the switch network.

C. Sensitivity analysis for the physical modelling of a long range repeater chain

NetSquid evaluates long-range repeater chains by combining detailed hardware models with asynchronous protocol simulation and statistical performance analysis. The studies expose distance-dependent trade-offs among fidelity, rate, hardware quality, and memory technology.

  • Repeater-chain modelling: NetSquid models repeater chains with reusable node and protocol specifications assigned across many nodes, while simulating local actions asynchronously.This modular, discrete-event approach supports detailed physical modelling and more complicated control-plane logic than simpler use cases.
  • Quantum-switch analysis: Quantum-switch capacity is measured as GHZ-states produced per second while varying buffer size, user link rates, and multipartite state size.For nine users, the study compares bipartite and four-partite entanglement and extends beyond analytically characterized cases.
  • Quantum-switch analysis: Switch capacity does not scale linearly with buffer size because the switch has only one link to each user.The green rate configuration also lacks a well-defined unbounded-buffer steady-state capacity under the stated Markov-chain stability condition.
  • Distance and hardware sensitivity: For improved hardware, repeaters raise rate but lower fidelity at short distances; from 750 km to 1500 km, they outperform no repeaters in both metrics.With near-term hardware, three repeaters instead perform worse in fidelity than the repeaterless configuration.
  • Protocol comparison: At 500 km, no repeaters achieve larger or equal fidelity across the studied hardware range, whereas at 800 km repeaters increase both rate and fidelity.Repeater schemes boost rate at both distances, and nested-with-distill is optimal among repeater schemes at high hardware quality.
  • Memory-technology comparison: EIT memories outperform AFC memories at short distances, but AFC memories outperform EIT memories beyond a crossover near 50 kilometers.The comparison changes only the quantum-memory component, illustrating how modularity supports hardware development studies.

E. Fast and scalable quantum network simulation

NetSquid targets accurate physical modelling, scalability to large networks, and fast multi-variate design analysis, while allowing users to prioritise these criteria by use case. Its benchmarks cover state-formalism performance and hardware scenarios involving atomic-ensemble memories and NV repeater chains.

  • NetSquid is designed to combine accurate physical modelling, large-network scalability, and runtime suitable for multi-variate design analyses.The paper notes that all criteria cannot always be jointly satisfied, so users can prioritise them for particular use cases.
  • Ket vectors and density matrices support universal quantum computation, while stabiliser tableaus and graph states with local Cliffords provide alternative state representations.The formalisms trade off modelling versatility, computation speed, and network-memory scalability.
  • 0.39 fidelity results when all approximately 15 NV hardware parameters are improved by a factor of 3 in the repeater-chain sensitivity analysis.The figure varies two-qubit gate fidelity, detection probability, induced storage-qubit noise, and visibility individually and in pairs.
  • Memoization caches repeated quantum-operator actions, reducing later applications to fast lookup and application of stored results.The benchmark includes GHZ-state generation and measurement, with ProjectQ ket vectors as a baseline comparison.
  • Atomic frequency comb and electronically induced transparency memories are compared by changing only the quantum-memory component in otherwise identical simulations.The comparison reports secret-key rate, QBER in the X and Z bases, and average attempts per successful end-to-end entanglement generation.
  • The available quantum-state formalisms are benchmarked using two use cases, including GHZ-state generation and quantum computation in a repeater chain.The results distinguish states split after measurement from states kept in place.

2. Benchmarking of event-driven simulations

NetSquid uses discrete-event simulation to handle time-dependent quantum-network behaviour and benchmarks event-driven repeater-chain simulations as networks grow. Its independent-run structure also supports parallel execution, while runtime remains constrained by per-core computational cost and memory.

  • NetSquid simulations repeatedly sample independent runs, making runtime reduction scale linearly with available processing cores when sufficient memory exists.
  • A single simulation run may process from a few thousand to millions of events, depending on network size, physical-model detail, and protocol duration.
  • PyDynAA provides the discrete-event engine for dynamically scheduling and handling events in NetSquid.NetSquid streamlines signals and messages between components through interconnecting ports.
  • At 1000 nodes, the components sub-package accounts for 30% of total runtime in the deterministic end-to-end entanglement benchmark.The benchmark uses ket-vector quantum computation and splits qubits after measurement to avoid exponential scaling with node count.
  • Discrete-event timing distinguishes NetSquid from simulators that do not accurately track time, which is important for studying time-dependent noise such as memory decoherence.
  • NetSquid’s modular framework supports large simulations and control-plane protocols, including networks of up to 1000 nodes.

2. Qubits and quantum computation

NetSquid represents qubits, hardware components, and control protocols as modular simulation entities connected through a discrete-event timeline. Its qubit layer supports multiple state formalisms, time-dependent noise, physical operations, and event-driven data collection.

  • Qubit objects share QState objects that grow and shrink as qubits interact or are measured, with multiple quantum-state formalisms implementing the QState interface.
  • Quantum operators can be memoized as sparse matrices, reducing repeated applications to sparse matrix multiplication on dense vectors or matrices.Memoization can also apply to Clifford operators and discretised continuous parameters.
  • All physical devices are component objects that can be recursively composed, allowing networks to contain nodes, connections, memories, and quantum or classical channels.
  • Protocol objects model network protocols and classical control-plane logic, directly interacting with the event timeline through callbacks or asynchronous event expressions.Event expressions can wait for port input, quantum-program completion, or a fixed duration.
  • NetSquid’s utilities control simulations, inspect timelines, collect event-driven data, and compute simulation statistics.
  • Time-dependent noise is applied when qubits are accessed after idling, using physical parameters such as relaxation time T1 and dephasing time T2.The NV model includes one communication qubit and multiple storage qubits.
  • Noisy operations are modelled as a perfect operation followed by a noise channel, with depolarising channels parameterised by operation fidelity for rotations and initialisation.

2. Simulation speedup via state insertion

For remote NV entanglement generation, NetSquid replaces infeasible explicit attempt-by-attempt simulation at larger distances with a stochastic state-insertion approach. The model preserves success probabilities, delays, heralding, and accumulated storage dephasing.

  • Explicitly simulating every entanglement-generation attempt becomes infeasibly slow at larger internode distances because attempt success decreases exponentially.
  • The entanglement model includes photon emission, lossy noisy transmission, imperfect midpoint measurements, and return of the measurement outcome to both nodes.
  • The successful attempt number k is sampled from a geometric distribution using the single-attempt success probability psucc.The elapsed time before the fresh state is placed on the electron spins is (k −1)·∆t, with ∆t including photon-emission and fibre-propagation delays.
  • Every generation attempt induces storage-qubit dephasing, accumulated and applied after successful entanglement generation.

3. How we choose improved hardware parameters

The simulations define hardware improvement factors relative to near-term NV parameters, applying them uniformly except to local-operation duration and fibre attenuation. These factors support hardware-performance assessment independently of NetSquid’s simulation setup.

  • Hardware improvement factors: k = 1 corresponds to near-term hardware, while larger k values represent improved error probabilities for defined parameters.The near-term values and individual improvement functions are specified in Supplementary Note 4.
  • Hardware improvement factors: Uniform improvement by k changes all hardware parameters except local-operation duration and fibre attenuation.The transmission loss parameter remains γ = 0.2 dB/km during simulations.
  • Protocol comparison: The NV repeater chain compares swap-asap with nested-with-distill protocols built from entanglement generation, storage, retrieval, distillation, and swapping.Distillation probabilistically improves remote nuclear-spin entanglement, while swapping converts adjacent pairs into a longer-distance pair.
  • Protocol comparison: NetSquid evaluates these protocols by simulating their hardware-dependent operations and classical communication procedures.The protocol blocks include waiting for entanglement-generation messages, memory-state mapping, probabilistic distillation checks, and swap corrections.

A. Qubits and their quantum state formalisms

NetSquid dynamically manages qubits and shared quantum states while supporting four state formalisms with different representational and runtime trade-offs. Stabiliser-tableau updates provide efficient simulation for Clifford operations, with complexity determined by qubit count.

  • Qubits and their quantum state formalisms: Qubit objects reference dynamically sized shared QState objects that merge on interaction and split after measurement or discard.This design tracks changing entanglement structure during a simulation rather than fixing one state size in advance.
  • Qubits and their quantum state formalisms: NetSquid supports four quantum-state formalisms, allowing simulations to switch between representations through a formalism-agnostic interface.The available representations include ket vectors, density matrices, stabiliser tableaus, and graph states with local Cliffords.
  • Stabiliser tableaus (STAB): The stabiliser formalism tracks commuting Pauli-group generators for stabiliser states rather than storing the full quantum state.Examples include generators for |0⟩, |00⟩, and (|00⟩+|11⟩)/√2.
  • Stabiliser tableaus (STAB): NetSquid stores stabiliser generators in a tableau whose rows encode generator information across X, Z, and phase entries.The tableau is the data structure used to update stabiliser states under supported operations.
  • Stabiliser tableaus (STAB): Stabiliser-tableau runtime is linear in qubit count for single- and two-qubit Clifford unitaries and cubic for single-qubit measurement.The algorithms support Clifford gates and computational-basis measurements.

Graph states with local Cliffords (GSLC)

The supplied passages describe NetSquid’s modular simulation architecture: event-driven execution connects physical components, software protocols, and benchmarked quantum-network workloads. The GSLC subsection itself represents stabiliser states through graph edges and local Clifford operations.

  • Graph states with local Cliffords (GSLC): A GSLC stabiliser state is represented by graph edges identifying controlled-Z operations and a list of n single-qubit Clifford operations.The graph state is determined by the edge set, while local Cliffords express the remaining stabiliser-state structure.
  • Discrete-event simulation: PyDynAA schedules events onto a simulation timeline, where entities register handlers that invoke callbacks when matching events occur.The engine advances sequentially from event to event.
  • Component modelling: NetSquid components model physical devices and can be composed from properties, ports, models, and subcomponents.Ports carry quantum and classical messages between components and their subcomponents.
  • Protocol modelling: Protocols model virtual behaviour layered over physical components, with local, node, and service subclasses adding execution scope or interface restrictions.This separates hardware entities from software behaviour in the simulation.
  • Quantum-computation benchmarking: NetSquid benchmarks quantum-circuit runtimes using GHZ-state generation and sequential measurements across alternative quantum-state formalisms.Timing isolates the circuit processes from setup code and reports the minimum of five repetitions.
  • Repeater-chain profiling: Event-driven runtime profiling uses a representative repeater chain with synchronised 100 kHz sources, 20 km node spacing, and time-dependent noise.The configuration includes depolarising noise in channels and memories and dephasing noise in gates.
  • Quantum-switch simulations: Quantum-switch simulations model a star network using leaf count k, shared-entanglement size n, generation rate μ, buffer size B, and memory coherence time T2.The switch retains bounded entanglement pairs and performs GHZ-basis measurements when enough distinct leaves are represented.

A. Physical network

The physical-network simulations model star-topology switch connections, repeater-link hardware, and NV-centre photon-mediated entanglement generation. They incorporate memory decoherence, optical loss, detection processes, and hardware parameter sets.

  • Physical network: The quantum switch uses a star topology with k ≥ 2 leaves, random entanglement-generation intervals at rate μ, and perfect bipartite source states.Quantum channels have zero delay, while processors provide enough memory for the run duration.
  • Physical network: Memory coherence is modelled through T2-dependent decoherence, while local unitary operations and single-qubit measurements are noiseless and instantaneous.The memory error probability follows the stated exponential coherence-time relation.
  • Physical network: The switch discards the oldest excess pair per leaf and performs an n-qubit GHZ-basis measurement when pairs from at least n distinct leaves are available.The measurement uses CNOT gates, a Hadamard gate, and computational-basis measurements.
  • NV elementary links: NV-centre entanglement generation uses a midpoint station with a 50:50 beam splitter and two non-number-resolving detectors.Each NV emits a photon after preparation of its electron in a bright-state-dependent superposition.
  • NV elementary links: The successful NV attempt produces a mixture of the desired entangled state and |00⟩, weighted by the bright-state parameter α.The simulations set α = 0.1 because fidelity is approximately maximal at lab-scale distances.
  • Imperfect detection: The NV setup assumes optical-cavity enhancement raises the zero-phonon-line probability from 3% to 46%.The fibre-transmission probability is determined by the internode distance and loss parameter.

b. Other sources of noise

The NV repeater model includes multiple physical noise sources affecting photon-mediated entanglement, spin coherence, and initialization. Parameters are converted into simulation-ready dephasing probabilities, including a nuclear-spin decay calibration.

  • Dark counts are modeled with a Poisson probability pdc = 1 −e−tw·λdark, using tw = 25 ns and λdark = 1 Hz.
  • Photon indistinguishability is represented by visibility V, set to 0.9, because imperfect overlap preserves which-way information.
  • Double excitation of the electron spin is modeled with occurrence probability pdexc = 0.06, representing emission of two photons after repeated excitation.
  • Photon phase uncertainty is modeled from a transmission-phase standard deviation σphase = 0.35 rad to compute dephasing.
  • Nuclear-spin dephasing from electron initialization is parameterized through N1/e, the number of pumping cycles required to shrink an equatorial Bloch vector to 1/e.
  • The single-qubit dephasing channel shrinks the equatorial Bloch-vector length by 1 −2p per application, enabling conversion between psingle and N1/e.
  • N1/e is set to 1400 electron-spin pumping cycles in the simulations.

d. Local processing parameters

The NV repeater simulations specify local hardware parameters and model repeater operations as asynchronous protocol actions over electron and nuclear spins. Swap-asap and nested-with-distill differ in when nodes generate, distill, and swap entanglement.

  • d. Local processing parameters: Electron-spin coherence uses T1 = 1 hour and T∗2 = 1.46s, while carbon nuclear-spin coherence uses T1 = 10 hours and T2 = 1 s.
  • d. Local processing parameters: The controlled-RX depolarizing probability is p = 0.02, corresponding to an effective circuit fidelity of 0.95 and gate fidelity FEC = 0.97.
  • d. Local processing parameters: Electron and carbon initialization fidelities are 0.99 and 0.997, respectively, while carbon Z-rotation fidelity is 0.999.
  • Operations for the building blocks: The protocol building blocks are store, retrieve, distill, and swap, with store mapping an electron state to a nuclear spin and retrieve reversing that mapping.
  • Repeater chain protocols: Swap-asap performs an entanglement swap as soon as a node holds pairs in both chain directions, whereas nested-with-distill applies distillation at each nesting level.
  • Repeater chain protocols: Nested actions are selected by chain position and entanglement span fn(k), with triggered nodes checking swaps, distillation, requests, and generation in order.
  • Correction tracking: Correction operators are tracked classically as Pauli operators rather than applied to imperfect hardware, avoiding gate noise and accommodating restricted NV processor topology.

A. Tracking correction operators during the NV repeater chain protocol

The correction-tracking proof maintains a target virtual Bell-state representation through entanglement generation, storage, distillation, and swapping. Distillation outcomes determine the resulting virtual state and measurement relation, while physical nuclear states require a Hadamard-based virtual transformation.

  • Correction tracking updates the virtual Bell-state representation after entanglement generation, distillation, and swapping so the target relation remains valid.
  • Entanglement generation sets Pauli corrections according to which detector clicks, using Z on one node when the non-target detector fires.
  • Store and retrieve move a qubit between memory positions without changing its associated correction Pauli.
  • During distillation, nodes apply Pn · Pe to electron spins, execute the circuit, exchange outcomes and Pn, and discard the nuclear pair after failure.
  • For swapping, node M performs a Bell-state measurement on A−M and M−B, sends correction information to A and B, and both update their local Paulis.
  • Proposition 1 states that distillation produces a specified nuclear-spin state while one measurement outcome is uniform and the other satisfies m2 = m1 · b · c.
  • The virtual nuclear state is related to the physical state by H ⊗H, and applying this transformation exchanges the Bell-state labels.
  • Proposition 2 gives virtual-state distillation outcomes with m1 uniformly random and m2 = m1 · b · d.

C. Correctness proof of the correction operator update for swap

The correction-operator update after entanglement swapping is derived by simplifying the intermediate node’s corrections and relating measurement outcomes to the endpoint corrections. The supplied material also specifies physical loss and Bell-state-measurement models used in the simulations.

  • Correctness proof: The swap proof assumes the intermediate node’s two correction operators can both be set to identity, leaving one communicated correction operator Q.The resulting correction is derived from measuring one qubit of each Bell pair.
  • Correctness proof: Measurement outcomes mearlier and mlater determine the Bell-state parameters through a = −mearliermlater and b = mlater.The mapping follows from applying the circuit to the electron-nuclear state, including a Hadamard for the rotated nuclear basis.
  • Physical model: Photon loss is modeled as a generalized amplitude-damping channel whose Kraus operator Ak represents exactly k lost photons.The loss probability depends on fibre attenuation, channel length, and coupling loss.
  • Physical model: The imperfect linear-optical Bell-state measurement incorporates photon distinguishability, detector efficiency, and dark counts through effective POVMs.These effective POVMs are obtained by weighting ideal measurement elements by the probabilities of detector outcomes under imperfections.

b. The figures of merit

The comparison uses secret key rate, quantum bit error rate, and attempts per successful end-node measurement as figures of merit. It evaluates two atomic-ensemble memory technologies under optimistic, shared simulation assumptions while accounting for their distinct physical characteristics.

  • Figures of merit: The comparison evaluates secret key rate for BB84, quantum bit error rate, and the average number of attempts per successful end-node measurement.QBER is obtained from wrong end-node correlations measured in the X and Z bases.
  • Figures of merit: The secret key rate uses the QBERs in the X and Z bases, binary entropy, and the average attempts per successful end-to-end entanglement generation.The factor 1/2 accounts for the probability that both BB84 end nodes choose the same basis.
  • Memory technologies: EIT and AFC memories represent contrasting designs: EIT offers superior efficiency with limited multiplexing, whereas AFC offers strong multiplexing potential.EIT uses an optical-control protocol; AFC uses an engineered absorption protocol.
  • Simulation parameters: The simulations use optimistic elementary-link and memory parameters, add noise parameters, and model a small probability of emitting two photon pairs.Common assumptions include 1000 source modes, p(1) = 0.9, and p(2) = 0.013.
  • Simulation parameters: The memory technologies are compared using parameters listed in Supplementary Table III.The table is identified as covering the two different atomic-ensemble memory technologies.
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