Efficiency supremacy of bit-encoded neural networks for Fock states
Oliver Kaestle, Alexander Carmele · arXiv (Cornell University) · 2021
Artificial neural networks have been established as a universally applicable tool in both science and industry. In the context of symmetric open quantum systems, specifically the restricted Boltzmann machine architecture has emerged as a natural and highly compressed representation of the density matrix for open spin-$1/2$ quantum systems via a direct mapping of spins to the visible neuron layer. Here we present a bit encoding scheme for a highly efficient and scalable representation of bosonic Fock number states in the restricted Boltzmann machine neural network architecture, extending its applicability beyond pure spin-$1/2$ open quantum systems. In contrast to common density matrix implementations, the complexity of the neural network scales only with the number of bit-encoded neurons rather than the maximum boson number. Crucially, in the high occupation regime its information compression efficiency is shown to surpass even maximally optimized density matrix implementations, where a projector method is used to access the sparsest Hilbert space representation available.