Continuous-variable Quantum Boltzmann Machine

TL;DR

This paper introduces a continuous-variable quantum Boltzmann machine (CVQBM) that leverages a CV photonic quantum computer and quantum imaginary time evolution to efficiently learn and generate complex probability distributions from classical and quantum data.

Contribution

It presents the first implementation of a CVQBM using CV quantum imaginary time evolution, enabling efficient distribution learning on photonic quantum computers.

Findings

High fidelity in distribution learning

Low Kullback-Leibler divergence achieved

Effective generation of classical and quantum data distributions

Abstract

We propose a continuous-variable quantum Boltzmann machine (CVQBM) using a powerful energy-based neural network. It can be realized experimentally on a continuous-variable (CV) photonic quantum computer. We used a CV quantum imaginary time evolution (QITE) algorithm to prepare the essential thermal state and then designed the CVQBM to proficiently generate continuous probability distributions. We applied our method to both classical and quantum data. Using real-world classical data, such as synthetic aperture radar (SAR) images, we generated probability distributions. For quantum data, we used the output of CV quantum circuits. We obtained high fidelity and low Kuller-Leibler (KL) divergence showing that our CVQBM learns distributions from given data well and generates data sampling from that distribution efficiently. We also discussed the experimental feasibility of our proposed CVQBM. Our method can be applied to a wide range of real-world problems by choosing an appropriate target distribution (corresponding to, e.g., SAR images, medical images, and risk management in finance). Moreover, our CVQBM is versatile and could be programmed to perform tasks beyond generation, such as anomaly detection.