Non‐Differentiable Leaning of Quantum Circuit Born Machine with Genetic Algorithm

The Quantum Circuit Born Machine (QCBM) is a generative quantum machine learning model that can be efficiently trained and run on the NISQ‐era quantum processors. It is likely that QCBM will be one of the first quantum machine learning models to find productive applications in quantitative finance as a powerful market generator. In this paper we test QCBM performance on a dataset of spot FX log‐returns (heavy‐tailed distribution) as well as specially constructed mixture of Normal distributions (which models spiky light‐tailed distribution). The QCBM has greater expressive power than comparable classical neural networks such as restricted Boltzmann machine (RBM) and, therefore, has potential to demonstrate quantum advantage by generating high‐quality samples from the learned empirical distribution of the market risk factors while using less computational resources than its classical counterpart. However, efficient training of QCBM remains a challenging problem. Traditional differentiable learning approach may not work well when the loss function is highly non‐smooth. In such cases it may be more efficient to use the non‐differentiable learning methods. This paper proposes a non‐differentiable learning approach to the training of QCBM based on genetic glgorithm (GA). The paper also presents results of the numerical experiments which compare performance of QCBM trained with GA against performance of the equivalent classical RBM and investigates the question of GA convergence as a function of QCBM architecture and the choice of algorithm's hyperparameters.