Sequential Hypothesis Testing for Continuously-Monitored Quantum Systems

This repository contains the numerical code supporting the research paper:

Sequential hypothesis testing for continuously-monitored quantum systems
Giulio Gasbarri, Matias Bilkis, Elisabet Roda-Salichs, and John Calsamiglia
Quantum 8, 1289 (2024)
https://quantum-journal.org/papers/q-2024-03-20-1289/

Overview

This codebase implements sequential hypothesis testing strategies for continuously-monitored quantum systems. The framework allows real-time analysis of measurement signals, enabling experiments to conclude as soon as the underlying hypothesis can be identified with a certified prescribed success probability. The implementation focuses on optomechanical systems under continuous homodyne detection in the Gaussian regime.

Key Features

• Sequential hypothesis testing: Real-time analysis of measurement signals with adaptive stopping criteria
• Quantum optomechanical simulations: Simulation of continuously-monitored quantum systems
• Multiple model support: Supports mechanical damping, frequency estimation, and force detection scenarios
• Efficient numerical integration: Optimized stochastic differential equation solvers using Numba JIT compilation
• Likelihood ratio computation: Real-time log-likelihood ratio tracking for hypothesis discrimination

Installation

Requirements

• Python 3.7+
• NumPy
• SciPy
• Numba
• Matplotlib
• tqdm

Setup

1. Clone the repository:

git clone https://github.com/matibilkis/qmonsprt.git
cd qmonsprt

2. Install dependencies:

pip install -r requirements.txt

Project Structure

qmonsprt/
├── numerics/              # Core numerical routines
│   ├── integration/       # Stochastic differential equation integration
│   │   ├── integrate.py           # Main integration routine for damping estimation
│   │   ├── integrate_freq_force.py  # Integration for frequency/force estimation
│   │   └── steps.py               # Numerical integration steps (Robler, Ikpw)
│   └── utilities/         # Utility functions
│       ├── misc.py                # General utilities and model definitions
│       ├── misc_freq.py           # Frequency estimation utilities
│       └── misc_force.py           # Force detection utilities
├── scripts/               # Execution and utility scripts
│   ├── run.py                    # Batch trajectory simulations
│   ├── mp_run*.py                # Multiprocessing execution scripts
│   └── *.py                      # Other utility scripts
├── analysis/              # Analysis and plotting scripts
│   ├── main_likelihood.py         # Likelihood analysis
│   ├── test_frequency.py          # Frequency estimation tests
│   ├── test_force.py              # Force detection tests
│   └── *_plots.py                 # Visualization scripts
├── tests/                 # Unit tests
│   ├── test_integration.py       # Integration tests
│   ├── test_utilities.py         # Utility function tests
│   └── test_euler_update.py      # Euler update tests
├── docs/                  # Documentation and LaTeX files
│   └── estim.tex                  # LaTeX source files
├── examples/              # Reference implementations
│   └── reference/giulio_julia/   # Julia reference implementations
└── HPC/                   # High-performance computing scripts
    └── condor_*.sub              # HTCondor submission scripts

Usage

Basic Integration

Run a single trajectory simulation:

python numerics/integration/integrate.py --itraj 1 --mode damping --dt 1e-4 --total_time 8.0

Batch Processing

Run multiple trajectories:

python scripts/run.py --seed 10 --mode damping --dt 1e-4 --total_time 50 --ppp 1000

Multiprocessing

Run parallel simulations:

python scripts/mp_run.py --itraj 1

Analysis

Analyze likelihood ratios and stopping times:

python analysis/main_likelihood.py

Mathematical Background

The code simulates continuously-monitored quantum systems described by stochastic differential equations:

dx_t = (A_θ - χ(Σ_t) C) x_t dt + χ(Σ_t) dy
dΣ_t = A_θ Σ_t + Σ A_θ^T + D - χ(Σ_t)^T χ(Σ_t)
dy = C x_t dt + C^{-1} dW_t

where:

• x_t is the system state (first moments)
• Σ_t is the covariance matrix (second moments)
• dy is the measurement outcome
• A_θ, C, D are system matrices parameterized by θ
• χ(Σ) is the Kalman gain

The sequential hypothesis test uses log-likelihood ratios to decide between hypotheses H₀ and H₁ in real-time.

Model Parameters

The system is parameterized by:

• γ: Damping rate
• ω: Frequency
• n: Thermal occupation number
• η: Measurement efficiency
• κ: Measurement strength

Testing

The repository includes a comprehensive test suite. To run tests:

Using pytest (recommended)

# Install test dependencies
pip install -r requirements.txt

# Run all tests
pytest tests/

# Run with coverage
pytest tests/ --cov=numerics --cov-report=html

# Run specific test file
pytest tests/test_integration.py -v

Using the test runner script

python3 tests/run_tests.py

Test Structure

• tests/test_integration.py: Tests for numerical integration routines (Ikpw, Robler_step)
• tests/test_utilities.py: Tests for utility functions (path handling, stopping times, etc.)
• tests/test_euler_update.py: Tests for Euler update and likelihood computation
• tests/conftest.py: Shared pytest fixtures and configuration

Citation

If you use this code in your research, please cite:

@article{Gasbarri2024sequential,
  doi = {10.22331/q-2024-03-20-1289},
  url = {https://doi.org/10.22331/q-2024-03-20-1289},
  title = {Sequential hypothesis testing for continuously-monitored quantum systems},
  author = {Gasbarri, Giulio and Bilkis, Matias and Roda-Salichs, Elisabet and Calsamiglia, John},
  journal = {{Quantum}},
  volume = {8},
  pages = {1289},
  month = mar,
  year = {2024}
}

Authors

• Giulio Gasbarri - Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona
• Matias Bilkis - Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona; Computer Vision Center, Universitat Autònoma de Barcelona
• Elisabet Roda-Salichs - Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona
• John Calsamiglia - Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona

License

This project is associated with the research published in Quantum journal under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.

Acknowledgments

This work was supported by research at the Universitat Autònoma de Barcelona. The codebase has been developed to support the research on sequential hypothesis testing for quantum systems.

Contributing

This is a research codebase. For questions or issues, please open an issue on GitHub or contact the authors.