The Hyperspin Machine in Nature Communications !

https://www.nature.com/articles/s41467-022-34847-9

From condensed matter to quantum chromodynamics, multidimensional spins are a fundamental paradigm, with a pivotal role in combinatorial optimization and machine learning. Machines formed by coupled parametric oscillators can simulate spin models, but only for Ising or low-dimensional spins. Currently, machines implementing arbitrary dimensions remain a challenge. Here, we introduce and validate a hyperspin machine to simulate multidimensional continuous spin models. We realize high-dimensional spins by pumping groups of parametric oscillators, and show that the hyperspin machine finds to a very good approximation the ground state of complex graphs. The hyperspin machine can interpolate between different dimensions by tuning the coupling topology, a strategy that we call “dimensional annealing”. When interpolating between the XY and the Ising model, the dimensional annealing substantially increases the success probability compared to conventional Ising simulators. Hyperspin machines are a new computational model for combinatorial optimization. They can be realized by off-the-shelf hardware for ultrafast, large-scale applications in classical and quantum computing, condensed-matter physics, and fundamental studies.

See also The hyperspin machine: simulating QCD models and dimensional annealing

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