Variational quantum algorithm for Gaussian discrete solitons and their boson sampling

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

https://arxiv.org/abs/2110.12379

https://link.aps.org/doi/10.1103/PhysRevA.106.013518

Quantum Machine Learning course on Github

Ph.D. course Quantum Machine Learning

Duration 20h (3CFU)
Scheduled at February or March 2022

Goals
1) introduction to phase space methods in quantum optics
2) introduction to quantum machine learning

Program
1) Methods in the phase space, characteristic function
2) Gaussian states and their transformations
3) Neural network representation of Gaussian states
4) Training of quantum machine learning models
5) Examples
Entanglement
Gaussian Boson sampling
Neural networks variational ansatz for quantum many-body

Exam (two options)
1) Colloquium on theoretical aspects
2) Coding examples

References
Barnett and Radmore, Methods in Theoretical Quantum Optics
ArXiv:2110.12379
ArXiv:2102.12142

Boson sampling solitons by quantum machine learning

https://arxiv.org/abs/2110.12379

We use a neural network variational ansatz to compute Gaussian quantum discrete solitons in an array of waveguides described by the quantum discrete nonlinear Schroedinger equation. By training the quantum machine learning model in the phase space, we find different quantum soliton solutions varying the number of particles and interaction strength. The use of Gaussian states enables measuring the degree of entanglement and the boson sampling patterns. We compute the probability of generating different particle pairs when varying the soliton features and unveil that bound states of discrete solitons emit correlated pairs of photons. These results may have a role in boson sampling experiments with nonlinear systems and in developing quantum processors to generate entangled many-photon nonlinear states.