Bloqade Simulation Software

• Bloqade Simulation Software is a dual-framework suite that automates optical Bloch equation derivations and blockchain simulation using reproducible, parameter-configurable models.
• It employs fixed-step RK4 integration for quantum optics and discrete-event simulation for blockchain networks, ensuring precise and scalable numerical solutions.
• The software emphasizes end-to-end reproducibility and modular extensibility, enabling its integration into diverse research workflows in both quantum and blockchain domains.

Bloqade Simulation Software refers to two unrelated simulation frameworks with overlapping nomenclature: (1) the Bloch Equation Generator (BEG), a computational tool for automating the derivation and numerical integration of multilevel optical Bloch equations; and (2) BlockSim (whose narrative documentation sometimes uses the variant “Bloqade”), a discrete-event simulation (DES) toolkit for blockchain system research. Each serves a specialized research audience and emphasizes end-to-end reproducibility, parameter configurability, and extensibility for complex quantum optics or blockchain models, respectively.

1. Mathematical Foundations and Underlying Models

Optical Bloch Equation Generator

The Bloch Equation Generator is grounded in the Liouville–von Neumann master equation for a quantum system with $N$ discrete levels, evolving under a total Hamiltonian $\hat H(t) = \hat H_0 + \hat H_I(t)$. Its density matrix $\hat\rho(t)$ evolves via

$$\partial_t \hat{\rho} = -\frac{i}{\hbar} [\hat H, \hat\rho].$$

For practical modeling in quantum optics, the internal Hamiltonian takes the form $$\hat H_0 = \sum_k \hbar\omega_k |k\rangle\langle k|$$, and the interaction with coherent fields is given by $\hat H_I = -\hat p E(t)$, with $E(t)$ decomposed into Fourier components.

The matrix-element equations, with relevant approximations (RWA for neglecting rapidly rotating terms), encode Rabi couplings, decay, and dephasing:

• Population ODEs: $$\partial_t \rho_{ii} = i\sum_k[\Omega_{ik}\sigma_{ki} - \Omega_{ki}\sigma_{ik}] + \sum_{j\neq i} \Gamma_{ji}\rho_{jj} - \sum_{j\neq i} \Gamma_{ij} \rho_{ii}$$
• Coherence ODEs: $$\partial_t \sigma_{ij} = i\sum_k[\Omega_{ik}\sigma_{kj} - \Omega_{kj}\sigma_{ik}] + (i\delta_{ij} - \gamma_{ij})\sigma_{ij},\ (i\neq j)$$

Relevant parameters:

• $\Omega_{ij}$: complex Rabi frequencies.
• $\delta_{ij}$: detunings.
• $\Gamma_{ij}$: spontaneous decay rates.
• $\gamma_{ij}$: coherence dephasing rates, given by $\frac{1}{2}\sum_k (\Gamma_{ik}+\Gamma_{jk})$.

Blockchain Simulation

BlockSim/Bloqade blockchain simulation operates at the intersection of stochastic process modeling, distributed systems, and economic incentive theory. The foundational mathematical elements include:

• Block generation as a Poisson process: inter-arrival times are $\operatorname{Exp}(\lambda)$.
• Message propagation modeled using exponential, log-normal, or empirical delay distributions.
• Incentive structures parameterized by block rewards, transaction fees, and specialized reward mechanisms (e.g., Ethereum uncle blocks).

2. Software Architecture and Algorithmic Workflow

BEG for Optical Bloch Equations

Upon user specification of system parameters and interaction structure, the BEG constructs a dependency graph over $N(N+1)/2$ independent ODE variables (populations and coherences). The code-generation sequence consists of:

• Symbolic assembly of right-hand side terms (Rabi coupling adjacency, decay, dephasing).
• Optionally applying the rotating wave approximation.
• Exporting C code implementing a fixed-step fourth-order Runge–Kutta (RK4) integrator for time ($t$) and frequency (detuning) domain solutions.
• For each detuning, the solver reinitializes the system and integrates until steady state.

BlockSim/Bloqade Blockchain Simulator

BlockSim’s core is a “Base Model” explicitly stratified into:

• Network Layer: Nodes, message propagation protocol (BroadcastProtocol), peer graph.
• Consensus Layer: Transaction, Block, ConsensusEngine (handles block creation, reception, and fork resolution).
• Incentives Layer: RewardModel (block rewards, transaction fees, special rewards).

Entities are mapped to modules/classes in Python; simulation is orchestrated via a discrete-event engine, with configurable parameters (node count, delay models, consensus mechanics) specified in configuration files.

3. User Interface, Input Configuration, and Code Generation

BEG User Interface

The browser-based interface (JS/HTML/CSS) provides:

• Levels panel: interactive creation/repositioning of $2\le N\le 30$ energy levels.
• Rabi Frequencies panel: assignment of field indices, amplitudes $E_m$, and phases.
• Decays panel: toggling/parameterizing spontaneous decay paths.
• RWA toggle.
• Numeric inputs for integration time, step size $h$, spectral width, and detuning granularity.
• On-demand LaTeX rendering of the ODE system; downloadable C code implementing the ODE integration kernels.

Exported Code Structure

File	Content	Functionality
bgen.h	Variable/array declarations	Model state definition
temporal_evolution.c	RK4 time-domain kernel	Main ODE solution loop
detuning.c	Sweeps detuning, records steady-state output	Frequency domain analysis

ODE variables are packed such that populations occupy $pop[1..N]$, with real and imaginary coherence parts stored in $pop[N+1..]$. The derivatives function (as in Listing 1) evaluates the full symbolic system as generated in the browser.

BlockSim Blockchain Configuration

Simulation parameters are defined in scripts or configuration files specifying network topology, consensus protocol, incentive mechanisms, simulation time, and replication count. Workflows:

• Edit config.py or YAML to set PARAMETERS.
• Execute python simulation invoking appropriate config; output is written as CSV and can be post-processed.

4. Representative Applications and Benchmarks

Quantum Optics Systems with BEG

• Two-Level System: Rabi oscillations and steady state approach for $\Gamma_{21}=2\pi\cdot5$ MHz, population accuracy $|ρ_{11} + ρ_{22} - 1|<5\times10^{-5}$ over 200 MHz sweep (Souza et al., 1 Jun 2025).
• $\Lambda$-Type System: Demonstration of coherent population trapping (CPT), electromagnetically induced transparency (EIT), and Autler–Townes effect. CPT yields dark-state coherence $σ_{13}\to-0.5$; EIT splitting modelled with variation of $Ω_{23}$.
• 12-level $^{87}$Rb Zeeman sublevels: Simulation of $\sigma^+$-polarized and $\pi$-excitation schemes, showing population funneling and manifold reduction analogous to a two-level system with <1% deviation for $Ω/Γ>0.5$.

Blockchain System Studies with BlockSim

• Reproduction of real-world Bitcoin (144 blocks/day, ≈0.04% stale rate, ≈2.7 tx/s) and Ethereum (6100 blocks/day, ≈12.6% uncle rate, ≈6 tx/s) metrics, within 95% CI of measured data (Alharby et al., 2020).
• Stale rate validation against prior literature within 10%.
• Uncle reward case study: Smallest miner’s reward share increases from 4.6% to 4.86% under Ethereum style uncle inclusion.

5. Strengths, Limitations, and Integration in Research Workflows

BEG

Key strengths:

• Full-stack workflow from symbolic model specification to optimized, ready-to-compile C code for up to $N=30$ levels ($N(N+1)/2=465$ ODEs).
• Interactive, web-based model construction.
• Automated dephasing computations, RWA toggle, high-precision integration.

Limitations:

• Only supports fixed-step RK4; lacks adaptive/implicit solvers.
• No in-browser spectral plotting in the free version (functionality planned).
• Decay is modeled phenomenologically; generalized Lindblad operators are not included.
• GPU/CUDA export is under development.

Typical workflow involves configuring multilevel schemes, downloading and compiling code, and embedding solvers within larger simulation/optimization environments (e.g., Python/Matlab pipelines).

BlockSim

Advantages:

• Modular extensibility enables users to subclass and implement new consensus protocols, delay models, and incentive schemes.
• Granularity selection between throughput-only and explicit fork modeling.
• Empirically validated performance.

Best practice recommendations include simulation warm-up, sufficient replication for statistical confidence, and resource-aware scaling.

6. Future Directions

For BEG, planned directions include in-browser spectral visualization, support for generalized Lindblad dynamics, and GPU-accelerated code generation. For BlockSim, ongoing improvements target expanded network-layer modeling, richer consensus/incentive extensions, and further validation on emerging blockchain architectures. As quantum-optics and blockchain-system complexity grows, these tools establish a technical foundation for systematic, reproducible simulation studies in their respective fields (Souza et al., 1 Jun 2025, Alharby et al., 2020).