Sample-efficient Quantum Born Machine through Coding Rate Reduction

TL;DR

This paper introduces a practical approach for training quantum Born machines using coding rate reduction, effectively mitigating mode collapse and improving scalability for generating binary images.

Contribution

It proposes combining the Maximal Coding Rate Reduction metric with class probability loss to enhance quantum generator training and reduce mode collapse.

Findings

MCR$^2$ combined with class probability loss resists mode collapse

Proposed techniques outperform previous QCBM training schemes on Bars and Stripes dataset

Method improves practicality and scalability of quantum generative models

Abstract

The quantum circuit Born machine (QCBM) is a quantum physics inspired implicit generative model naturally suitable for learning binary images, with a potential advantage of modeling discrete distributions that are hard to simulate classically. As data samples are generated quantum-mechanically, QCBMs encompass a unique optimization landscape. However, pioneering works on QCBMs do not consider the practical scenario where only small batch sizes are allowed during training. QCBMs trained with a statistical two-sample test objective in the image space require large amounts of projective measurements to approximate the model distribution well, unpractical for large-scale quantum systems due to the exponential scaling of the probability space. QCBMs trained adversarially against a deep neural network discriminator are proof-of-concept models that face mode collapse. In this work we investigate practical learning of QCBMs. We use the information-theoretic \textit{Maximal Coding Rate Reduction} (MCR$^2$) metric as a second moment matching tool and study its effect on mode collapse in QCBMs. We compute the sampling based gradient of MCR$^2$ with respect to quantum circuit parameters with or without an explicit feature mapping. We experimentally show that matching up to the second moment alone is not sufficient for training the quantum generator, but when combined with the class probability estimation loss, MCR$^2$ is able to resist mode collapse. In addition, we show that adversarially trained neural network kernel for infinite moment matching is also effective against mode collapse. On the Bars and Stripes dataset, our proposed techniques alleviate mode collapse to a larger degree than previous QCBM training schemes, moving one step closer towards practicality and scalability.