Variational learning of quantum ground states on spiking neuromorphic hardware

Abstract

We train a neuromorphic hardware chip to approximate the ground states of quantum spin models by variational energy minimization. Compared to variational artificial neural networks using Markov chain Monte Carlo for sample generation, this approach has the advantage that the neuromorphic device generates samples in a fast and inherently parallel fashion. We develop a training algorithm and apply it to the transverse field Ising model, showing good performance at moderate system sizes (N ≤ 10). A systematic hyperparameter study shows that scalability to larger system sizes mainly depends on sample quality which is limited by parameter drifts on the analog neuromorphic chip. The learning performance shows a threshold behavior as a function of the number of variational parameters of the ansatz, with approximately 50 hidden neurons being sufficient for representing critical ground states up to N = 10. The 6+1-bit resolution of the network parameters does not limit the reachable approximation quality in the current setup. Our work provides an important step towards harnessing the capabilities of neuromorphic hardware for tackling the curse of dimensionality in quantum many-body problems.

Three learning stages and accuracy–efficiency tradeoff of restricted Boltzmann machines

“…Moreover, the computational complexity of these methods is usually higher because additional substeps are necessary to produce a new Markov-chain sample. While a detailed quantitative analysis is missing, the overall evaluation efficiency (e.g., the required computational resources) will presumably not be improved in general [25], and probably the only remedy to circumvent the sampling problem could be novel computing hardware such as neuromorphic chips [49][50][51][52][53], "memcomputing machines" [54], or quantum annealers [55,56].…”