QDMesh

Modular Quantum Drone & QKD Simulation Framework in Wolfram Language

This post introduces QDMesh, a modular Wolfram Language framework for simulating quantum-enabled drone networks, atmospheric optical propagation, QKD (Quantum Key Distribution), energy consumption, swarm intelligence, and quantum-verified key management.The framework is composed of six independent modules: 1. Core 2. Physics 3. Power 4. Crypto 5. Swarm 6. KMSEach module can be loaded separately and is implemented exclusively in Wolfram Language.Below you will find: 1.Description of every module 2.Complete source code 3.An integrated simulation scriptThis post is self-contained. All code can be executed directly in a Wolfram notebook.

1. Core Module

The Core module defines the fundamental physical constants and parameters of a quantum drone. These values act as the baseline for optical simulation, energy computation, and cryptographic protocol modeling.
Code: QDMesh/Core.wl

In[]:=

BeginPackage["QDMesh`Core`"];$Wavelength;$Aperture;$DroneMass;$BatteryCapacity;Begin["`Private`"];$Wavelength=1550*10^-9;$Aperture=0.10;$DroneMass=4.5;$BatteryCapacity=500000;End[];EndPackage[];

2. Physics Module

The Physics module models atmospheric turbulence and optical distortion for free-space quantum links.It computes realistic estimations of: 1.Refractive index structure parameter (Cn²) 2.Scintillation index 3.Beam wander variance

In[]:=

BeginPackage["QDMesh`Physics`"];AtmosphericState::usage="AtmosphericState[alt, wind, dist, tempGradient] computes Cn2, scintillation, \and beam wander variance for a given flight segment.";Begin["`Private`"];AtmosphericState[alt_,wind_,dist_,tempGradient_]:=Module[{cn2,scint,wander},cn2=1*10^-14/(1+alt/1000)+10^-16wind;scint=0.5*cn2*dist;wander=cn2*dist^2*0.001+tempGradient*10^-7;<|"Cn2"cn2,"Scintillation"scint,"BeamWander_Var"wander|>];End[];EndPackage[];

3. Power Module

The Power module estimates total drone power usage considering propulsion, transmission load, and onboard computing.

In[]:=

BeginPackage["QDMesh`Power`"];CalculateConsumption::usage="CalculateConsumption[velocity, isTransmitting, isComputing] returns total \power consumption in watts.";Begin["`Private`"];CalculateConsumption[vel_,tx_,comp_]:=Module[{base,txP,compP},base=0.5vel^3+80;txP=If[tx,50,0];compP=If[comp,20,0];base+txP+compP];End[];EndPackage[];

4. Crypto Module

The Crypto module simulates quantum key distribution protocols (BB84 and E91) and includes a post-quantum signature generator.It produces: 1. Raw bit count 2.QBER 3.Final key length 4.Protocol metadata

In[]:=

BeginPackage["QDMesh`Crypto`"];RunProtocol::usage="RunProtocol[type, loss, nPhotons] simulates a QKD protocol (BB84 or E91).";SignPQC::usage="SignPQC[msg] returns a post-quantum signature.";Begin["`Private`"];RunProtocol[type_,loss_,n_]:=Module[{raw,qber,final},raw=Round[n*(1-loss)];qber=0.02+loss*0.1+If[type=="E91",-0.005,0];final=Round[raw*(1-qber-0.01)];<|"Protocol"type,"RawBits"raw,"FinalKey"final,"QBER"qber|>];SignPQC[msg_]:=Hash[msg,"SHA3-512"];End[];EndPackage[];

5. Swarm Module

The Swarm module models coordinated behavior among multiple drones for secure communication and anomaly detection.Functions include: 1.Fusion of QBER and wind estimates 2.Threat-level prediction based on node reputation

In[]:=

BeginPackage["QDMesh`Swarm`"];CooperativeFusion::usage="CooperativeFusion[data] fuses QBER and wind values across drones.";PredictThreat::usage="PredictThreat[qber, reputation] classifies potential threats.";Begin["`Private`"];CooperativeFusion[data_List]:=Module[{qbers,winds},qbers=Mean[data[[All,"QBER"]]];winds=Mean[data[[All,"Wind"]]];<|"GlobalQBER"qbers,"GlobalWind"winds|>];PredictThreat[qber_,rep_]:=If[qber>0.03||rep<0.7,"THREAT","SAFE"];End[];EndPackage[];

6. KMS Module (Key Management System)

Integrated Framework Demonstration

Additional Scientific Experiments and Visual Demonstrations Using QDMesh

This section provides extended, visually oriented, scientifically motivated experiments that demonstrate how each module of the QDMesh framework can be used for simulation, validation, visualization, and preliminary research prototyping.

All experiments below operate only with the modules defined earlier and require no additional components.

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Experiment 1 — Atmospheric Turbulence Profile Visualization

This experiment generates a vertical profile of the refractive-index structure parameter Cn² across altitudes from 0 to 3 km. It demonstrates how environmental modeling affects QKD performance.

This plot illustrates how turbulence decreases with altitude, influencing beam wander and scintillation in free-space quantum links.

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Experiment 2 — Beam Wander vs Temperature Gradient (Sensitivity Map)

This two-dimensional study shows the sensitivity of beam wander variance as a function of both altitude and temperature gradient.

This heatmap helps visualize how environmental gradients impact quantum link stability.

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Experiment 3 — Energy Consumption vs Airspeed

This experiment models the relationship between drone forward velocity and total power consumption, assuming constant transmission and negligible computational load.

This plot can be used to determine optimal cruise speed for QKD missions.

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Experiment 4 — BB84 vs E91 Performance Across Link Distance

This experiment compares two QKD protocols under increasing free-space distance.

This benchmark shows protocol robustness as optical attenuation increases.

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Experiment 5 — Swarm-Based Threat Monitoring Simulation

This experiment simulates ten drones, each reporting local QBER and wind measurements, then computes global fusion and threat levels.

This experiment illustrates cooperative anomaly detection appropriate for dynamic drone mesh networks.

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Final Note

The modules presented in this framework were manually designed with simplified physics and system abstractions to ensure they can be easily extended, adapted, and refined for more precise or domain-specific research needs. The example scripts and the descriptive text accompanying each module were generated with the assistance of artificial intelligence solely for time-efficiency purposes, and may contain minor inaccuracies.

The overall framework structure and conceptual direction were inspired by:

Hernandez Barreto, A. D., Velasco Campos, M. F., & Morales Escobar, K. Y. (2025–2026).
Dynamic Drone Mesh Networks for Scalable Quantum Key Distribution in Challenging Environments (Translated version).
DOI: 10.5281/zenodo.17718867.

These modules and experimental components will continue to be expanded and refined for upcoming simulations and conceptual studies on distributed quantum communication in dynamic or challenging environments.