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The self-learning Metropolis-Hastings algorithm is a powerful Monte Carlomethod that, with the help of machine learning, adaptively generates aneasy-to-sample probability distribution for approximating a givenhard-to-sample distribution. This paper provides a new self-learning MonteCarlo method that utilizes a quantum computer to output a proposaldistribution. In particular, we show a novel subclass of this general schemebased on the quantum Fourier transform circuit; this sampler is classicallysimulable while having a certain advantage over conventional methods. Theperformance of this "quantum inspired" algorithm is demonstrated by somenumerical simulations.

Quantum self-learning Monte Carlo with quantum Fourier transform sampler