Quantum approximate Bayesian computation for NMR model inference - Sels, Dries; Dashti, Hesam; Mora, Samia; Demler, Olga; Demler, Eugene (Nature machine intelligence, 2020)
Recent technological advances may lead to the development of small-scale quantum computers that are capable of solving problems that cannot be tackled with classical computers. A limited number of algorithms have been proposed and their relevance to real-world problems is a subject of active investigation. Analysis of many-body quantum systems is particularly challenging for classical computers due to the exponential scaling of the Hilbert space dimension with the number of particles. Hence, solving the problems relevant to chemistry and condensed-matter physics is expected to be the first successful application of quantum computers. In this Article, we propose another class of problems from the quantum realm that can be solved efficiently on quantum computers: model inference for nuclear magnetic resonance (NMR) spectroscopy, which is important for biological and medical research. Our results are based on three interconnected studies. First, we use methods from classical machine learning to analyse a dataset of NMR spectra of small molecules. We perform stochastic neighbourhood embedding and identify clusters of spectra, and demonstrate that these clusters are correlated with the covalent structure of the molecules. Second, we propose a simple and efficient method, aided by a quantum simulator, to extract the NMR spectrum of any hypothetical molecule described by a parametric Heisenberg model. Third, we propose a simple variational Bayesian inference procedure for estimating the Hamiltonian parameters of experimentally relevant NMR spectra. Currently available quantum hardware is limited by noise, so practical implementations often involve a combination with classical approaches. Sels et al. identify a promising application for such a quantum–classic hybrid approach, namely inferring molecular structure from NMR spectra, by employing a range of machine learning tools in combination with a quantum simulator.