Simulation of a Dynamic, RuleSet-based Quantum Network

Takaaki Matsuo

REVIEW 3 major objections 4 minor 73 references

Simulation of a Dynamic, RuleSet-based Quantum Network

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A RuleSet-based protocol can raise average Bell-pair fidelity from 0.675 to about 0.865 on a 10 km quantum link.

desk verdict A genuinely useful protocol idea buried in a thesis whose quantitative claims rest on a Pauli-only simulation that needs rerunning before the numbers are trusted. read the letter →

arxiv 1908.10758 v1 pith:GLPDR2CE submitted 2019-08-26 quant-ph cs.NI

Takaaki Matsuo This is my paper · ORCID

classification quant-phcs.NI

keywords RuleSetprotocolquantumlinkbootstrappingentanglementpurificationrepeaternetworksMarkov-ChainMonte-CarlosimulationtomographyMeetInTheMiddleBell-pairfidelity

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This thesis tries to establish that distant quantum nodes can coordinate link bootstrapping—tomography plus recurrent entanglement purification—without exchanging a classical message for every step, by pre-distributing RuleSets that trigger local actions when conditions hold. The payoff would be a quantum Internet in which nodes autonomously learn link quality and purify Bell pairs, with only measurement outcomes travelling over the classical channel. Using a Markov-Chain Monte-Carlo simulator with noisy memories, channels, gates and detectors modeled on current hardware, the thesis reports that the Recurrent Single selection - Single error purification protocol lifts average fidelity from $F_r=0.675$ to about $F_r=0.865$ on a 10 km MeetInTheMiddle link with 100 memory qubits per node. It also argues that no single purification method wins everywhere: on noisier, longer channels double-selection purification is better, and switching methods mid-recurrence can improve both fidelity and throughput.

What carries the argument

The load-bearing object is the RuleSet: a set of Rules, each containing a Condition (one or more Clauses) and an Action, pre-distributed at connection setup so nodes execute operations locally when conditions are met. The Rule Engine interprets and executes these rules in real time, selecting the oldest available resource and exchanging only measurement results. The other central mechanism is recurrence purification built from purification rounds such as Ss-Sp (single selection, single error), Ds-Sp (double selection, single error), and their double-error variants, combined with full-state link-level tomography. The simulation tracks qubit states through a continuous-time Markov chain with seven memory states (clean, X, Z, Y, excited, relaxed, completely mixed) and five channel states (clean, X, Z, Y, lost), and propagates Pauli errors through circuits; this error-propagation model is what makes the fidelity numbers concrete.

What would settle it

Run the same two-node 10 km MeetInTheMiddle bootstrapping with full density-matrix evolution (not Pauli-only propagation) under identical noise parameters; if the final fidelity after RSs-Sp falls below about 0.865, the reported gain is an artifact of the error model. A hardware experiment measuring Bell-pair fidelity before and after RSs-Sp recurrence on such a link would settle the claim directly.

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Extended reading notes

Core claim

The central claim is that a RuleSet-based communication protocol can make quantum link bootstrapping dynamic and largely autonomous. Concretely, the thesis claims that on a 10 km MeetInTheMiddle link, with 100 memory qubits per node and noise parameters taken from realistic hardware, the Recurrent Single selection - Single error purification (RSs-Sp) protocol raises the average reconstructed fidelity of generated Bell pairs from $F_r=0.675$ to approximately $F_r=0.865$. The thesis also claims that the best purification choice is link-dependent: for noisier or longer channels, where errors accumulate faster than purification gain, double-selection purification (e.g., RDs-Sp) becomes advantageous, and switching from RDs-Sp to RSs-Sp in the middle of a recurrence can improve both fidelity and throughput. The bootstrapping process, therefore, should include a check of which purification works best for a particular link.

Load-bearing premise

The simulation assumes that purification circuits only need to track Pauli errors, so real-world excitation, relaxation, and completely mixed errors are not caught by the purification logic; if those non-Pauli errors are substantial, the predicted fidelity gain and throughput numbers do not directly carry over.

Editorial extensions

If this is right

Link bootstrapping can run without a classical handshake per operation: nodes act on pre-distributed RuleSets and only send measurement outcomes, cutting coordination traffic.
Recurrent Ss-Sp purification can bring a 10 km link's Bell-pair fidelity from 0.675 to about 0.865, a level usable for applications that require high-quality shared entanglement.
On longer or noisier links, purification gain may be overtaken by error accumulation, so single-selection purification is not universally optimal; double-selection purification becomes the better choice there.
Switching purification method mid-recurrence (e.g., from RDs-Sp to RSs-Sp) can increase both final fidelity and throughput, implying bootstrapping should adaptively choose the purification strategy.
Tomography with at least 7,000 measurement outcomes keeps reconstructed-fidelity standard deviation below 0.015, and roughly 20,000 outcomes give sub-1% accuracy, setting a practical sample-size budget for link monitoring.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural extension the author leaves implicit is closed-loop adaptation: the reconstructed fidelity from each tomography round could feed back into the RuleSet selection, making the bootstrapping protocol itself a learning controller over purification strategies.
Because only Pauli errors are stochastically propagated through purification circuits, real hardware with significant $T_1$ relaxation or leakage would likely show lower fidelity than the reported 0.865; a direct test would replace Pauli-only propagation with full Kraus-operator evolution and compare the outcomes.
The RuleSet abstraction is not tied to bootstrapping: the same condition/action structure could coordinate entanglement swapping, routing decisions, or application-level requests, potentially reducing classical latency across the whole quantum network stack.
The reported trade-off between fidelity gain and resource consumption suggests an optimization problem—choosing purification depth per link to maximize throughput at a target fidelity—that the thesis identifies but does not formally solve.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

This is a Master's thesis, but it contains a concrete protocol proposal—RuleSets for distributed coordination of quantum operations—plus a simulator and evaluation. The abstract's fidelity gain (0.675 to 0.865) is the eye-catcher, but that number is simulation output, not hardware reality, and it depends on assumptions the thesis itself flags.

What's actually new: the RuleSet construct (condition/action rules distributed at connection setup), its application to link bootstrapping with recurrent purification, and adaptive switching between purification protocols (e.g., RDs-Sp to RSs-Sp) based on measured error rates. The pseudocode is concrete, the simulator is built on OMNeT++ with explicit memory/channel/gate/detector error models, and the evaluation averages 25 runs with error bars. The paper is also unusually candid: it explicitly says only Pauli errors are propagated through circuits, and that this makes output fidelity pessimistic and resource generation rate optimistic.

Soft spots, in proportion. The quantitative claims—0.865 fidelity, throughput figures, and the recommendation to switch purification methods adaptively—are not directly supported for real hardware because non-Pauli states (excited, relaxed, mixed, lost) appear in the input model but are not stochastically detected by the purification circuits. The paper's directional caveat is reasonable but not derived; it does not tell you how the two purification protocols compare under those omitted channels. Also, the simulations assume ideal classical channels, zero gate times, and an artificial 50 ms memory lifetime. The abstract's phrase "real world quality hardware" overstates all this. And no code or data is released, so independent reproduction requires reimplementation.

None of that kills the protocol idea. The RuleSet approach to minimizing classical coordination traffic is worth discussing, and adaptive purification switching is a sensible engineering hypothesis. But the paper earns peer review as a protocol proposal with preliminary simulation support, not as a hardware-realistic performance claim.

Recommendation: send it to a serious referee. A competent reviewer will ask for a full density-matrix validation of the purification circuits (or at least a sensitivity analysis with non-Pauli channels) and for released code/data. If those are addressed, the RuleSet angle would be a useful contribution to the quantum networking literature.

Referee Report

3 major / 4 minor

Summary. This manuscript, a Keio University master's thesis posted on arXiv, proposes a RuleSet-based protocol for autonomously coordinating quantum-network operations (purification, tomography, resource selection) between distant nodes with limited classical messaging. It also presents an OMNeT++-based discrete-event simulator that models a two-node MeetInTheMiddle/SenderReceiver link with noisy memories, channels, gates, and detectors, and evaluates recurrent purification (RSs-Sp, Ds-Sp, etc.) combined with full-state link-level tomography. The headline result is that for a 10 km MeetInTheMiddle link with 100 memory qubits per node, the RSs-Sp recurrence raises the average input fidelity from about F_r=0.675 to about F_r=0.865; for noisier, longer links, double-selection purification is reported to be advantageous, and switching mid-recurrence can improve fidelity and throughput.

Significance. If the quantitative claims were fully supported, the paper would be a useful contribution to quantum-network control-plane design: it gives concrete pseudocode (Algorithms 1–5), a modular node/BSA simulator architecture, explicit error models with default parameters (Table 6.1), and Monte Carlo results with error bars over 25 runs. The authors are candid about several modeling limitations, including the artificial 50 ms memory lifetime and the Pauli-only propagation through purification circuits. The main significance, however, is conditional on the noise model; the claimed fidelity gain and protocol ranking are not yet established for the full error model that the simulator's generators describe.

major comments (3)

[Section 6 (first paragraph) and Section 5.3] The headline fidelity gain (abstract; Figs. 6.11–6.13) is computed with only Pauli errors propagated through the purification circuits, even though the memory and channel generators (Eqs. 5.2 and 5.4; Sections 5.3.1–5.3.2) explicitly include excited, relaxed, completely mixed, and lost states. The text acknowledges this and calls the output fidelity pessimistic and the rate optimistic, but that directional statement is not a proof, and it does not justify the protocol-ordering conclusion (e.g., switching from RDs-Sp to RSs-Sp at L=20 km in Fig. 6.14), because omitted non-Pauli events can be rejected or accepted differently by the two circuits. The authors should either rerun the simulation with full density-matrix propagation, or restrict all quantitative claims to a stated Pauli-only error model and remove the unqualified 'real world quality hardware' wording from the abstract.
[Section 4.2 and Section 6.3] The paper's central value proposition is that RuleSets coordinate distant nodes 'with minimal classical packet transmission,' but no evaluation of classical traffic is reported. Section 6 measures reconstructed fidelity and resource-generation throughput only; there are no packet counts, no baseline protocol for comparison, and no latency/bandwidth analysis. The protocol may well reduce classical messages, but that claim is currently unsupported by the simulation results.
[Abstract, Table 6.1, and Section 5.1] Several parameter choices limit the 'real world hardware' characterization in the abstract. In particular, the memory lifetime is an artificial 50 ms (footnote to Table 6.1), classical channels are assumed ideal (Section 5.1.1), gate times are negligible (Section 5.1.2), and clock synchronization is perfect (Section 5.1.7). These are legitimate simulation assumptions, but the abstract's phrase 'modeled on real world quality hardware' overstates what the simulation establishes. The headline numbers should be presented as predictions of this specific model, with these assumptions stated whenever the numbers are quoted.

minor comments (4)

[Section 5.3.1 and Table 6.1] The generator matrices in Eqs. (5.2) and (5.4) are written with abbreviated row sums and no explicit per-transition rates; please provide the full numerical generator used for the default parameters so that the simulation can be reproduced.
[Section 6, opening paragraph] The term 'Markov-Chain Monte-Carlo' is a misnomer: the simulator performs Monte Carlo trials with Markov-chain error models, not Markov-Chain Monte-Carlo sampling. Please reword.
[Section 2.9.2, Eq. (2.148)] Fidelity defined as Tr[rho_a rho_i] is the standard pure-state fidelity only when the ideal state rho_i is pure; since all applications here use a pure ideal Bell state, this is fine, but the definition should state that restriction.
[Section 1.3] The thesis-structure description says Chapter 6 contains 'some details' and Chapter 7 contains the main results, but the evaluation is actually presented in Chapter 6; update the structure description to match the body.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the claimed fidelity improvement is a Monte-Carlo output, not a fitted input or a self-citation chain.

full rationale

The paper's main claim—that RSs-Sp raises fidelity from about 0.675 to about 0.865 over a 10 km MeetInTheMiddle link—is the measured output of an independent Markov-Chain Monte-Carlo simulation, not a quantity fed into the simulation. The simulator models memory, channel, gate, detector, and BSA errors with parameters drawn from external hardware references; the recurrence purification circuits (Algorithms 2 and 3) are executed on generated Bell pairs, and the resulting fidelity and throughput are recorded after the runs. No parameter is fitted to the claimed output and then renamed a prediction. The only self-citation that appears, the author's bachelor's thesis, is used for background theory and is not load-bearing; the related Oka thesis [52] is cited as prior work on recurrence purification under Pauli errors, but the present paper's conclusion is not derived from that citation. The explicit limitation in Section 6—'we only propagate Pauli errors through circuits... incapable of stochastically detecting excited/relaxed/completely mixed errors. Hence, our simulation generates a pessimistic output fidelity, and an optimistic output resource generation rate'—is an honest modeling caveat about the scope of the numerical results, not a circular step: the omitted non-Pauli channels affect accuracy but are not assumed as the target result. Because the central numerical claims are self-contained simulation outputs and no equation is reduced to its own input, no circularity is present.

Assumptions & free parameters 14 free parameters · 8 assumptions · 0 invented entities

The central quantitative claims rest on 14 simulation parameters, most taken from cited hardware works but two explicitly artificial (50 ms memory lifetime and 100:1 excitation/relaxation ratio), and on a set of idealized system assumptions: perfect clocks, ideal classical channels, arbitrary local multi-qubit gates, negligible gate times, and exact photon emission timing. The paper self-identifies the Pauli-only error propagation as a limitation. No new physical entities are introduced.

free parameters (14)

Fiber refractive index = 1.44
Input parameter from [64]; sets photon propagation speed in the channel model.
Fiber Pauli error rate per km = 0.03 per km (X/Y/Z total)
Input parameter from [64]; directly sets the base Bell pair fidelity entering purification.
Fiber photon loss rate per km = 0.04501 per km (0.2 dB/km)
Input parameter from [64]; controls entanglement generation rate and loss-induced errors.
Memory Pauli error rate per second = 1/3 per second
Used in the memory Markov chain, from [65]; decides how fast stored Bell pairs degrade during purification and tomography.
Memory lifetime = 50 ms
Called artificial in the paper; excitation/relaxation ratio set to 100:1. Strongly affects whether purification gain outruns memory decay, especially at 20 km.
Emission probability into zero phonon line = 0.46
From [66]; part of the memory-to-fiber emission probability and thus the resource generation rate.
Photon collection efficiency = 0.49
From [67,68]; combined with emission probability to set memory-to-fiber coupling.
Photon detector efficiency = 0.8
From [68]; affects detected entanglement generation rate.
Photon detector darkcount rate = 10 per second
From [68]; can cause false entanglement detection when photons are lost.
Photon detector recovery time = 1 ns
From [69]; limits maximum generation attempt rate.
Single-qubit gate error rate = 0.0005
From [70]; each gate stochastically produces X/Y/Z error.
Multi-qubit gate error rate = 0.02
From [71]; CNOT/CZ operations in purification circuits inject errors that limit achievable fidelity.
Measurement error rate = 0.05
From [72]; affects tomography outcomes and purification post-selection.
Memory qubits per QNIC = 100
Buffer size in the central 10 km result; constrains how many purification attempts can run before timeout.

assumptions (8)

domain assumption All NICs are connected to ideal classical channels with no error, infinite bandwidth, and the same latency as corresponding QNICs.
Stated in Section 5.1.1. The protocol's benefit is minimal classical messaging, but assuming ideal classical channels removes real-world latency and bandwidth constraints.
domain assumption Rule engines have perfectly synchronized clocks between nodes.
Stated in Section 5.1.7 and in the Chapter 4 assumptions. Underpins simultaneous photon emission and synchronized purification actions.
domain assumption Nodes can perform arbitrary multi-qubit operations between qubits in any local QNICs.
Stated in Section 5.1.2. Removes architecture restrictions that could prevent the purification circuits from running.
domain assumption Gate times are negligible.
Stated in the Chapter 6 opening and in Section 5.1.2. Lets memory error wait times be dominated by classical latency only.
domain assumption Nodes emit photons at the exact timing provided by the BSA controller.
Stated in Section 5.2.2. The BSA coordination scheme relies on this.
domain assumption Reliable, in-order timely delivery of classical messages.
Stated in the Chapter 4 assumptions. No packet loss or reordering in the coordination protocol.
ad hoc to paper Only Pauli errors are propagated through purification circuits.
Chapter 6 states this explicitly to reduce computation time; the paper admits it makes the output fidelity pessimistic and the resource generation rate optimistic.
domain assumption Memory errors evolve as a memoryless continuous-time Markov chain over seven state classes.
Section 5.3.1 defines the Q matrix and uses pi(t) = pi(0) Q^t. This is a standard modeling choice but is not validated against physical memory dynamics.

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Cite this review

Pith. "Pith review of Simulation of a Dynamic, RuleSet-based Quantum Network." pith.science (2026). https://pith.science/paper/GLPDR2CE

@misc{pith2026190810758,
  author       = {Pith},
  title        = {Pith review of: Simulation of a Dynamic, RuleSet-based Quantum Network},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GLPDR2CE}},
  note         = {Machine review of arXiv:1908.10758}
}

abstract

Similar to the classical Internet, the quantum Internet will require knowledge regarding link qualities used for purposes such as optimal route selection. This is commonly accomplished by performing link-level tomography with or without purification -- a.k.a. quantum link bootstrapping. Meanwhile, the gate selection and the resource (Bell pair) selection for a task must be coordinated beforehand. This thesis introduces the RuleSet-based communication protocol aimed for supporting the autonomous coordination of quantum operations among distant nodes, with minimal classical packet transmission. This thesis also discusses the RuleSet-based quantum link bootstrapping protocol, which consists of recurrent purifications and link-level tomography, evaluated over a Markov-Chain Monte-Carlo simulation with noisy systems modeled on real world quality hardware. Given a 10km MeetInTheMiddle based two-node system, each with 100 memory qubits ideally connected to the optical fiber, the Recurrent Single selection - Single error purification (RSs-Sp) protocol is capable of improving the fidelity from an average input $F_{r}=0.675$ to approximately $F_{r}=0.865$. The system gets noisier with longer channels, in which case errors may develop faster than the purification gain. For a noisier system with a longer channel length, the double selection-based purification shows an advantage for improving the fidelity.

Figures

Figures reproduced from arXiv: 1908.10758 by the authors.

**Figure 2.1.** Quantum State described on a Bloch Sphere [PITH_FULL_IMAGE:figures/full_fig_p015_2_1.png] view at source ↗

**Figure 2.2.** Basic flow of quantum gate operation 2.4.1 Single Qubit Gates The most important operators for quantum computing are called the Pauli operators. The Pauli-X gate is the equivalent of the classical NOT gate. The gate can be performed on a single qubit state and swaps the probability amplitude of |0i and |1i. X = 0 1 1 0 (2.21) X [PITH_FULL_IMAGE:figures/full_fig_p017_2_2.png] view at source ↗

**Figure 2.3.** Circuit representation of a Pauli-X gate [PITH_FULL_IMAGE:figures/full_fig_p017_2_3.png] view at source ↗

Figures from the paper (64 more)

**Figure 2.4.** Figure 2.4: Circuit representation of a Pauli-Y gate [PITH_FULL_IMAGE:figures/full_fig_p018_2_4.png]

**Figure 2.5.** Figure 2.5: Circuit representation of a Pauli-Z gate [PITH_FULL_IMAGE:figures/full_fig_p018_2_5.png]

**Figure 2.6.** Figure 2.6: Circuit representation of an Hadamard gate [PITH_FULL_IMAGE:figures/full_fig_p018_2_6.png]

**Figure 2.7.** Figure 2.7: Circuit representation of a S gate T [PITH_FULL_IMAGE:figures/full_fig_p019_2_7.png]

**Figure 2.8.** Figure 2.8: Circuit representation of a T gate Two S gates and an X gate can be used to construct a Y gate: Y = SXS† . A gate that rotates the quantum state by 180 degrees is not affected by the rotational direction; clockwise or anti-clockwise. As an S gate performs a rotation …

**Figure 2.9.** Figure 2.9: Circuit representation of a Measurement gate and its byproduct operator [PITH_FULL_IMAGE:figures/full_fig_p020_2_9.png]

**Figure 2.10.** Figure 2.10: Circuit representation of a Controlled-NOT gate [PITH_FULL_IMAGE:figures/full_fig_p021_2_10.png]

**Figure 2.11.** Figure 2.11: Circuit representation of a Controlled-Z gate [PITH_FULL_IMAGE:figures/full_fig_p022_2_11.png]

**Figure 2.12.** Figure 2.12: A quantum circuit generating a GHZ state (refer to subsection 2.6.3) of three [PITH_FULL_IMAGE:figures/full_fig_p028_2_12.png]

**Figure 2.13.** Figure 2.13: Example circuits of an Hadamard gate and a CNOT gate. [PITH_FULL_IMAGE:figures/full_fig_p032_2_13.png]

**Figure 2.14.** Figure 2.14: Propagation of stabilizers in the creation of a 3-qubit GHZ state. Stabilizer I is [PITH_FULL_IMAGE:figures/full_fig_p034_2_14.png]

**Figure 2.15.** Figure 2.15: Simple quantum circuit of quantum teleportation [PITH_FULL_IMAGE:figures/full_fig_p035_2_15.png]

**Figure 2.16.** Figure 2.16: Simple quantum circuit of quantum teleportation without byproduct operations [PITH_FULL_IMAGE:figures/full_fig_p036_2_16.png]

**Figure 2.17.** Figure 2.17: Visualized model of quantum teleportation. At the end of the operation, the red [PITH_FULL_IMAGE:figures/full_fig_p036_2_17.png]

**Figure 2.18.** Figure 2.18: Simple quantum circuit of entanglement swapping [PITH_FULL_IMAGE:figures/full_fig_p037_2_18.png]

**Figure 2.19.** Figure 2.19: Visualized model of entanglement swapping [PITH_FULL_IMAGE:figures/full_fig_p038_2_19.png]

**Figure 2.20.** Figure 2.20: Visualized model of entanglement purification [PITH_FULL_IMAGE:figures/full_fig_p038_2_20.png]

**Figure 2.21.** Figure 2.21: Architecture of a simple two-node quantum repeater network. [PITH_FULL_IMAGE:figures/full_fig_p043_2_21.png]

**Figure 2.22.** Figure 2.22: Bell measurement using a beam splitter and photon detectors. [PITH_FULL_IMAGE:figures/full_fig_p044_2_22.png]

**Figure 2.23.** Figure 2.23: Error propagation of Hadamard gate 36 [PITH_FULL_IMAGE:figures/full_fig_p045_2_23.png]

**Figure 2.24.** Figure 2.24: Error propagation of Controlled-Not gate [PITH_FULL_IMAGE:figures/full_fig_p046_2_24.png]

**Figure 2.25.** Figure 2.25: Error propagation of Controlled-Z gate The measurement outcome depends on the quantum state, and thus a measurement error leads to an erroneous feedforward operation. Therefore measurement errors in MBQC, explained in section 2.10, also propagate to other qubits th…

**Figure 2.26.** Figure 2.26: Error propagation of measurement Other unfixable errors In general, Pauli errors can be detected and discarded through purification (see section 2.8.3), or corrected through error correction. However, there exists a type of errors that cannot be 37 [PITH_FULL_IMAGE…

**Figure 2.27.** Figure 2.27: 2D resource state generation The technique to map an unknown quantum state from one qubit to another is known as one-bit teleportation (see [PITH_FULL_IMAGE:figures/full_fig_p048_2_27.png]

**Figure 2.28.** Figure 2.28: Quantum circuit for one-bit teleportation [PITH_FULL_IMAGE:figures/full_fig_p048_2_28.png]

**Figure 2.29.** Figure 2.29: One-bit teleportation to Measurement-based Quantum Computing [PITH_FULL_IMAGE:figures/full_fig_p049_2_29.png]

**Figure 2.30.** Figure 2.30: Measurement-based single qubit unitary operation [PITH_FULL_IMAGE:figures/full_fig_p049_2_30.png]

**Figure 2.31.** Figure 2.31: Measurement-based CNOT operation 40 [PITH_FULL_IMAGE:figures/full_fig_p049_2_31.png]

**Figure 2.32.** Figure 2.32: Topological transition by measurements on 1D cluster states [PITH_FULL_IMAGE:figures/full_fig_p050_2_32.png]

**Figure 2.33.** Figure 2.33: Topological transition by measurements on 2D cluster states [PITH_FULL_IMAGE:figures/full_fig_p051_2_33.png]

**Figure 3.1.** Figure 3.1: Chinese satellite beaming down entangled photons to earth [PITH_FULL_IMAGE:figures/full_fig_p053_3_1.png]

**Figure 3.2.** Figure 3.2: The MeetInTheMiddle model. This requires a stand-alone BSA node in between [PITH_FULL_IMAGE:figures/full_fig_p054_3_2.png]

**Figure 3.3.** Figure 3.3: The SenderReceiver model. The BSA is installed inside one endpoint. [PITH_FULL_IMAGE:figures/full_fig_p054_3_3.png]

**Figure 3.4.** Figure 3.4: The MidpointSource model. The BSA is installed inside both nodes, with a [PITH_FULL_IMAGE:figures/full_fig_p055_3_4.png]

**Figure 3.5.** Figure 3.5: Required functionality for each layer network stack as in [51]. [PITH_FULL_IMAGE:figures/full_fig_p055_3_5.png]

**Figure 3.6.** Figure 3.6: Layered architecture for quantum communication as in [51]. [PITH_FULL_IMAGE:figures/full_fig_p056_3_6.png]

**Figure 3.7.** Figure 3.7: Procedures of quantum link bootstrapping. Here, the fidelity is the reconstruction [PITH_FULL_IMAGE:figures/full_fig_p057_3_7.png]

**Figure 3.8.** Figure 3.8: Procedure of quantum link bootstrapping with purification. [PITH_FULL_IMAGE:figures/full_fig_p058_3_8.png]

**Figure 4.1.** Figure 4.1: Flow chart of resource generation. This process is looped to continuously gen [PITH_FULL_IMAGE:figures/full_fig_p060_4_1.png]

**Figure 4.2.** Figure 4.2: Node A generating and distributing RuleSets done at connection setup time. In [PITH_FULL_IMAGE:figures/full_fig_p061_4_2.png]

**Figure 4.3.** Figure 4.3: Bias in knowledge regarding the state of resources. Node C receives the suc [PITH_FULL_IMAGE:figures/full_fig_p062_4_3.png]

**Figure 4.4.** Figure 4.4: An example structure of a RuleSet. The resource allocated in the second Rule [PITH_FULL_IMAGE:figures/full_fig_p062_4_4.png]

**Figure 4.5.** Figure 4.5: Flow chart of the hardware monitor working on link-level tomography. RD is [PITH_FULL_IMAGE:figures/full_fig_p063_4_5.png]

**Figure 5.1.** Figure 5.1: The Quantum Internet. Different networks are operated under different tech [PITH_FULL_IMAGE:figures/full_fig_p070_5_1.png]

**Figure 5.2.** Figure 5.2: Quantum node architecture. 5.1.1 Network Interface Card (NIC) A NIC is connected to the classical channel, and is capable of forwarding classical packets out to the channel. Assumption: All NICs are connected to ideal classical channels – no error and infinite bandwi…

**Figure 5.3.** Figure 5.3: 63 [PITH_FULL_IMAGE:figures/full_fig_p072_5_3.png]

**Figure 5.4.** Figure 5.4: Example topology based on the routing table in Tab.5.3. Here, there is only one [PITH_FULL_IMAGE:figures/full_fig_p074_5_4.png]

**Figure 5.5.** Figure 5.5: Flow chart of the connection setup including three nodes. RE is Rule Engine and [PITH_FULL_IMAGE:figures/full_fig_p074_5_5.png]

**Figure 5.6.** Figure 5.6: BSA node architecture. Classical communications, shown as dashed arrows, will [PITH_FULL_IMAGE:figures/full_fig_p075_5_6.png]

**Figure 5.7.** Figure 5.7: Bell measurement with a Y error on the received photon. [PITH_FULL_IMAGE:figures/full_fig_p078_5_7.png]

**Figure 5.8.** Figure 5.8: Bell measurement with a lost error on the received photon. [PITH_FULL_IMAGE:figures/full_fig_p079_5_8.png]

**Figure 6.2.** Figure 6.2: Change in the accuracy of the reconstructed fidelity relative to the actual fidelity. [PITH_FULL_IMAGE:figures/full_fig_p083_6_2.png]

**Figure 6.3.** Figure 6.3: Single selection - Single error (X) purification (Ss-Sp). Consumes a single Bell [PITH_FULL_IMAGE:figures/full_fig_p084_6_3.png]

**Figure 6.** Figure 6: , the X error from qubit E and qubit F will propagate to qubit A and qubit B through [PITH_FULL_IMAGE:figures/full_fig_p084_6.png]

**Figure 6.4.** Figure 6.4: Single selection - Double error (XZ) purification (Ss-Dp). Consumes two Bell [PITH_FULL_IMAGE:figures/full_fig_p084_6_4.png]

**Figure 6.5.** Figure 6.5: Double selection - Single error (X) purification (Ds-Sp). Consumes a single Bell [PITH_FULL_IMAGE:figures/full_fig_p085_6_5.png]

**Figure 6.6.** Figure 6.6: Double selection - Double error (XZ) purification (Ds-Dp). Consumes two Bell [PITH_FULL_IMAGE:figures/full_fig_p085_6_6.png]

**Figure 6.7.** Figure 6.7: Impact of the MeetInTheMiddle channel length on the reconstructed fidelity with [PITH_FULL_IMAGE:figures/full_fig_p086_6_7.png]

**Figure 6.8.** Figure 6.8: Impact of the channel distance on the channel throughput with and without per [PITH_FULL_IMAGE:figures/full_fig_p087_6_8.png]

**Figure 6.9.** Figure 6.9: Recurrence purification protocol based on single selection X purification and Z [PITH_FULL_IMAGE:figures/full_fig_p089_6_9.png]

**Figure 6.10.** Figure 6.10: Flowchart of the quantum link bootstrapping. The termination process due [PITH_FULL_IMAGE:figures/full_fig_p090_6_10.png]

**Figure 6.14.** Figure 6.14: Switching RDs-Sp to RSs-Sp over L = 20km. a) Pattern 1 consists of one round RDs-Sp and four rounds of RSs-Sp. Purification methodology switches at Np = 1. b) Pattern 2 consists of two rounds RDs-Sp and three rounds of RSs-Sp. Purification methodology switches at Np…

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Pith tools

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