Application of Quantum Circuit Learning for Statistical Safety Evaluation

To reduce the computational demand in the best estimate plus uncertainty (BEPU) analysis, an accurate and inexpensive machine learning model is expected to be used to replace the high-fidelity RELAP5 code for rapid determination of the uncertainties on the figure of merit of interest. Quantum circuit learning is an algorithm that can work on NISQ (noisy intermediate-scale quantum) computers. In this paper, the applicability of optimization methods that are popular in deep learning to quantum circuit learning was investigated in order to construct a model that is effective even with the hardware limitations of NISQ computers. Quantum circuits were implemented by Qulacs and defined as a custom layer in PyTorch. SGD was used as an optimization method. When SGD was used, convergence on training data was slow, but generalization performance on non-training data was good. It was concluded that by appropriately selecting the algorithm and the hyperparameters of optimization method of deep learning framework, a learning process can be achieved with good generalization performance and a learning model can be constructed with good prediction accuracy for the 95% cumulative probability value.