All-Optical Scalable Spatial Coherent Ising Machine

Networks of optical oscillators simulating coupled Ising spins have been recently proposed as a heuristic platform to solve hard optimization problems. These networks, called coherent Ising machines (CIMs), exploit the fact that the collective nonlinear dynamics of coupled oscillators can drive the system close to the global minimum of the classical Ising Hamiltonian, encoded in the coupling matrix of the network. To date, realizations of large-scale CIMs have been demonstrated using hybrid optical-electronic setups, where optical oscillators simulating different spins are subject to electronic feedback mechanisms emulating their mutual interaction. While the optical evolution ensures an ultrafast computation, the electronic coupling represents a bottleneck that causes the computational time to severely depend on the system size. Here, we propose an all-optical scalable CIM with fully programmable coupling. Our setup consists of an optical parametric amplifier with a spatial light modulator (SLM) within the parametric cavity. The spin variables are encoded in the binary phases of the optical wave front of the signal beam at different spatial points, defined by the pixels of the SLM. We first discuss how different coupling topologies can be achieved by different configurations of the SLM, and then benchmark our setup with a numerical simulation that mimics the dynamics of the proposed machine. In our proposal, both the spin dynamics and the coupling are fully performed in parallel, paving the way towards the realization of size-independent ultrafast optical hardware for large-scale computation purposes.

https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.16.054022

https://arxiv.org/abs/2111.06737

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.

Quantum machine learning and boson sampling

Training Gaussian boson sampling by quantum machine learning

published in Quantum Machine Intelligence 3, 26 (2021)

Pseudocode

We use neural networks to represent the characteristic function of many-body Gaussian states in the quantum phase space. By a pullback mechanism, we model transformations due to unitary operators as linear layers that can be cascaded to simulate complex multi-particle processes. We use the layered neural networks for non-classical light propagation in random interferometers, and compute boson pattern probabilities by automatic differentiation. This is a viable strategy for training Gaussian boson sampling. We demonstrate that multi-particle events in Gaussian boson sampling can be optimized by a proper design and training of the neural network weights. The results are potentially useful to the creation of new sources and complex circuits for quantum technologies.

https://doi.org/10.1007/s42484-021-00052-y