Variational quantum algorithm for Gaussian discrete solitons and their boson sampling

TL;DR

This paper introduces a neural network-based variational quantum algorithm to find and analyze Gaussian quantum solitons in waveguide arrays, exploring their entanglement and potential for boson sampling and quantum processing.

Contribution

It develops a novel neural network variational approach for quantum solitons, enabling the study of their properties and entanglement in nonlinear quantum systems.

Findings

Different soliton solutions found by varying particles and interactions

Gaussian states used to measure entanglement and particle correlations

Bound states emit correlated particle pairs

Abstract

In the context of quantum information, highly nonlinear regimes, such as those supporting solitons, are marginally investigated. We miss general methods for quantum solitons, although they can act as entanglement generators or as self-organized quantum processors. We develop a computational approach that uses a neural network as a variational ansatz for quantum solitons in an array of waveguides. By training the resulting phase-space quantum machine learning model, we find different soliton solutions varying the number of particles and interaction strength. We consider Gaussian states that enable measuring the degree of entanglement and sampling the probability distribution of many-particle events. We also determine the probability of generating particle pairs and unveil that soliton bound states emit correlated pairs. These results may have a role in boson sampling with nonlinear systems and in quantum processors for entangled nonlinear waves.