High-order-quantum-trajectory-simulation

# High-order Quantum Trajectory Simulation This repository contains Python scripts for simulating quantum trajectoriesusing higher-order methods from the literature, and for analysing theresulting conditioned states via trace-distance measures (error analysis). The code is intended to reproduce the numerical simulations used in our workon high-order quantum trajectory reconstruction. --- ## Usage The simulation consists of two main steps. ### Step 1: Generate true trajectories and measurement records Run:python True_Data_Generation.py This script generates: - True quantum trajectories - Coarse-grained measurement records $I_t$ and $\phi_t$ The generated data are saved and used as input for the second step. ### Step 2: Simulate conditioned quantum trajectoriesRun:python Trajectory_simulation.py This script: - Reconstructs quantum trajectories conditioned on the previously generated - coarse-grained records - Implements existing (lower- and higher-order) trajectory simulation methods - Performs trace-distance analysis and generates histograms for comparison Example of simulation procedures: ### Modifying the measurement processTo obtain results for different measurement schemes, users may modify: - The measurement operator $\hat c$ - The corresponding initial quantum state These are explicitly defined in the scripts and can be adjusted directly. ### Details for simulation examples. - Example 1. Use operator $\hat c = \sqrt{\gamma/2}\hat \sigma_z$ with the initial state $|+x\rangle$ for spin 1/2 system. - Example 2. Use operator $\hat c = \sqrt{\gamma}\hat \sigma_-$ with the initial state $|+x\rangle$ for spin 1/2 system. - Example 3. Use operator $\hat c = \sqrt{\gamma}\hat \sigma_-$ with the initial state $|+x\rangle$ for spin 1 system. - Example 4. Use operator $\hat c = \sqrt{\gamma}\hat \sigma_-$ with the initial state $|+x\rangle$ for spin 3/2 system. - Example 5. Use operator $\hat c = \sqrt{\gamma/2}\hat \sigma_z$ with the initial state $|+x\rangle$ for spin 1 system. ### Numerical results (error analysis) ### Notes - The scripts are designed to be run sequentially. - Numerical parameters and random seeds can be adjusted within the scripts. - The computational cost depends on the system dimension and time resolution.