Category: Nonlinear Photonics

The hyperspin machine: simulating QCD models and dimensional annealing

https://arxiv.org/abs/2203.16190

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 study NP-hard graphs of hyperspins. 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 impressively 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.

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

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.