Efficient bit encoding of neural networks for Fock states

TL;DR

This paper introduces a novel bit encoding scheme for bosonic Fock states in neural networks, significantly improving scalability and efficiency over traditional density matrix methods, especially at high occupation numbers.

Contribution

The authors develop a scalable bit encoding approach for Fock states in neural networks, reducing complexity and surpassing density matrix methods in high occupation regimes.

Findings

Complexity scales with number of bit-encoded neurons

Outperforms density matrix implementations in high occupation regimes

Achieves efficient information compression for bosonic states

Abstract

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. 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.