Quantum Trajectory Reconstruction via Weak Measurement and Probabilistic Inference

This project introduces a computational framework for quantum trajectory reconstruction using weak measurements and probabilistic inference.

In standard quantum mechanics, physical systems are described by a wavefunction, and observable quantities are inherently probabilistic. As a result, particle trajectories are not directly accessible. This work proposes an operational approach in which trajectories are treated as latent variables inferred from noisy measurement data.

The framework combines three core components:

A numerical solver for the time-dependent Schrödinger equation (using FFT-based split-operator methods)

A weak measurement model that simulates continuous, noisy observations of the system

Inference engines, including Sequential Monte Carlo (particle filtering) and recurrent neural networks, to reconstruct the most probable trajectory

The central idea is to reformulate quantum dynamics as an inference problem over hidden states, where the goal is to estimate the trajectory that best explains the observed measurements.

This approach does not violate the principles of quantum mechanics, including the Principe d'incertitude de Heisenberg, but instead provides a new computational lens through which quantum systems can be analyzed.

Potential applications include:

Quantum sensing and metrology

Quantum control and error correction

Hybrid AI-quantum systems

Advanced simulation of open quantum systems

The project is fully reproducible and open-source, with modular architecture designed for research extensibility.