Quantum Boltzmann Machines

The qbm Python package is designed for training and analyzing quantum Boltzmann machines (QBMs) using either a simulation or a D-Wave quantum annealer. The QBM implemented here is based on the work in Quantum Boltzman Machine by Amin et al. [1]. This package originated as part of the thesis Quantum Boltzmann Machines: Applications in Quantitative Finance.

Table of Contents

• Installation
  • Conda Environment
• Usage
  • Basic Configuration
  • BQRBM Model
    • Instantiation
    • Training
    • Sampling
    • Saving and Loading
  • Example
• References

Installation

The qbm package can be installed with

pip install qbm

Usage

Basic Configuration

The qbm package is mainly configured around the project directory, which can be set with the QBM_PROJECT_DIR environment variable. Once the environment variable is set one can use the qbm.utils.get_project_dir() function to get a path object to the directory.

BQRBM Model

The BQRBM, or bound-based quantum restricted Boltzmann machine, is a quantum Boltzmann machine that has intra-layer restrictions and is trained via maximization of the log-likelihood lower bound. The model currently only has the ability to train in the specific case where s_freeze = 1, i.e., when it reduces to a classical RBM trained with quantum assistance, because estimating the effective inverse temperature is nontrivial for the general case.

All of the arguments to the methods below are further explained in their respective docstrings.

Instantiation

A BQRBM model can be instantiated as (for example)

model = BQRBM(
    V_train,
    n_hidden,
    A_freeze,
    B_freeze,
    beta_initial=1.0,
    simulation_params={"beta": 1.0},
    seed=0,
)

One needs to choose whether or not they want to train a model using a simulation or an annealer, and this is done by passing either simulation_params or annealer_params. Whichever is passed decides how the model is trained.

Training

The model can be trained by running

model.train(
    n_epochs=100,
    learning_rate=1e-1,
    learning_rate_beta=1e-1,
    mini_batch_size=10,
    n_samples=10_000,
    callback=None,
)

Sampling

The model can generate samples by running

model.sample(
    n_samples,
    answer_mode="raw",
    use_gauge=True,
    binary=False,
)

Saving and Loading

The model can be saved with

model.save("/path/to/model.pkl")

and loaded again with

model = BQRBM.load("/path/to/model.pkl")

Example

An example notebook can be found here

References

[1] Mohammad H. Amin et al. “Quantum Boltzmann Machine”. In: Phys. Rev. X 8 (2 May 2018), p. 021050. doi: 10.1103/PhysRevX.8.021050. url: https://link.aps.org/doi/10.1103/PhysRevX.8.021050.