QD-HMC

This repository contains the code and plotting functions to recreate the Quantum Dynamical Hamiltonian Monte Carlo (QD-HMC) algorithm. It is built on TensorFlow-Quantum (TFQ), TensorFlow-Probability (TFP), and Continuous-Variable TensorFlow-Quantum (CV-TFQ).

This repo also contains an implementation of the QMCMC algorithm from this paper, which can be found in the MH directory.

Set Up

To begin using the code, simply clone the repository and ensure you have a virtual environment set up with all the requirements.

Usage

QD-HMC is heavily integrated into TFP, and the usage is similar to the built in HMC. Just specify a few required hyperparameters and you are good use it just as you would classical HMC. Note that the run_chain function that is used when .run_hmc() is called is decorated with @tf.function, which gives substantial speed benefits.

test_q = HMC(log_prob, kernel_type='quantum', precision=precision, num_vars=n)
samples, sample_mean, sample_stddev, is_accepted, results = test_q.run_hmc(1000, 100)

Check out the examples folder to see more demonstrations and complex use cases of QD-HMC.

There are a few limitations of note. Because this is built on CV-TFQ, there are limitations to the CV operators. Specifically, they are not ammenable to the usual numpy/TF broadcasting and vectorization. This requires all functions to be explicitly indexed, e.g. lambda x : -x - x**2 will not work but np.sum([-1 * x[i] for i in range(n)] + [-1 * x[i]**2 for i in range(n)]) will. These ops also have a few other quirks worth noting, -op is not allowed and you must used -1 * op. The only mathematical operations supported are the basic addition, subtraction, multiplication, and exponentiation (by positive integer). More complex functions must be approximated using these function.

Citation

If you use or build upon QD-HMC in your work, please cite our technical paper:

@misc{lockwood2024quantum,
      title={Quantum Dynamical Hamiltonian Monte Carlo}, 
      author={Owen Lockwood and Peter Weiss and Filip Aronshtein and Guillaume Verdon},
      year={2024},
      eprint={2403.01775},
      archivePrefix={arXiv},
      primaryClass={quant-ph}
}