Generative Learning with Quantum Models

Generative machine learning (ML) tasks are prominent across a wide range of industries,

and are difficult to tackle even with some of the best classical ML approaches that we have

available. By introducing quantum models for these tasks, we have already seen promising results

for quantum advantage with respect to the model’s expressibility, trainability, and most recently,

generalization performance. While being the golden standard for ML and a widely investigated

topic in supervised learning, generalization in the unsupervised regime has previously been

difficult to evaluate and thus, overlooked in the investigations of quantum generative models.

Here, we provide a summary of progress towards advantage with respect to some of the

most prominent quantum generative models - the Quantum Circuit Born Machine (QCBM) and its

quantum-inspired version, the Tensor Network Born Machine (TNBM). We first present a

framework that provides a robust assessment of classical and quantum generative models for

their generalization capabilities. Subsequently, we utilize the framework to conduct the first deepdive

investigation into the QCBM’s and TNBM’s generalization performance, using models with

varied model ansatze and training dataset sizes. We present an advantage of TNBMs over stateof-

the-art classical models such as Generative Adversarial Networks (GANs) and we show for the

first time that QCBMs exhibit good generalization performance with increasing circuit depth, on

instances with training sets corresponding to a small fraction of the overall data space.

Additionally, we see that both, quantum-inspired tensor-network models and QCBMs are able to

effectively learn bias in its training data and generate unseen samples that are higher quality than

those in the training set. Lastly, we discuss the near-term opportunities and challenges for

quantum generative models as we scale and move towards practical applications.