Quantum self-learning Monte Carlo and quantum-inspired Fourier transform sampler

The self-learning metropolis-Hastings algorithm is a powerful Monte Carlo method that, with the help of machine learning, adaptively generates an easy-to-sample probability distribution for approximating a given hard-to-sample distribution. This paper provides a new self-learning Monte Carlo method that utilizes a quantum computer to output a proposal distribution. In particular, we show a novel subclass of this general scheme based on the quantum Fourier transform circuit; when the dimension of the input to QFT corresponding to the low-frequency components is not large, this sampler is classically simulable while having a certain advantage over conventional methods. The performance of this quantum-inspired algorithm is demonstrated by some numerical simulations.