The quantum restricted Boltzmann machine is universal for quantum computation

Yusen Wu, Fei Gao

Published 2020-05-25Version 1

The challenge posed by the many body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the exponential complexity of the many body wave function. Simulating the large-scale wave function with highly entanglement is always accompanied by the computationally intractable even using the most powerful classical computers. In this thesis, we demonstrate that the 2-Local Quantum Restricted Boltzmann Machine (2LQRBM) can efficiently represent the many-body wave function on the noisy intermediate scale quantum (NISQ) devices, and we also propose a proof that 2LQRBM is universal for quantum computation task.To the best of our knowledge, prior works related to the QRBM do not propose the explicit bound that single layer QRBM can depict. Utilizing this novel scheme, we successfully compute the wavefunctions for the notable cases of physical interest, such as the ground state as well as the Gibbs state (thermal state) of a molecule on the superconductor quantum chip with an affordable error. Experimental results confirm our method.