Large-scale photonic Ising machine by spatial light modulation

Quantum and classical physics can be used for mathematical computations that are hard to tackle by conventional electronics. Very recently, optical Ising machines have been demonstrated for computing the minima of spin Hamiltonians, paving the way to new ultra-fast hardware for machine learning. However, the proposed systems are either tricky to scale or involve a limited number of spins. We design and experimentally demonstrate a large-scale optical Ising machine based on a simple setup with a spatial light modulator. By encoding the spin variables in a binary phase modulation of the field, we show that light propagation can be tailored to minimize an Ising Hamiltonian with spin couplings set by input amplitude modulation and a feedback scheme. We realize configurations with thousands of spins that settle in the ground state in a low-temperature ferromagnetic-like phase with all-to-all and tunable pairwise interactions. Our results open the route to classical and quantum photonic Ising machines that exploit light spatial degrees of freedom for parallel processing of a vast number of spins with programmable couplings.Comment: https://journals.aps.org/prl/accepted/7007eYb7N091546c41ad4108828a97d5f92006df

Adiabatic evolution on a spatial-photonic Ising machine

Combinatorial optimization problems are crucial for widespread applications but remain difficult to solve on a large scale with conventional hardware. Novel optical platforms, known as coherent or photonic Ising machines, are attracting considerable attention as accelerators on optimization tasks formulable as Ising models. Annealing is a well-known technique based on adiabatic evolution for finding optimal solutions in classical and quantum systems made by atoms, electrons, or photons. Although various Ising machines employ annealing in some form, adiabatic computing on optical settings has been only partially investigated. Here, we realize the adiabatic evolution of frustrated Ising models with 100 spins programmed by spatial light modulation. We use holographic and optical control to change the spin couplings adiabatically, and exploit experimental noise to explore the energy landscape. Annealing enhances the convergence to the Ising ground state and allows to find the problem solution with probability close to unity. Our results demonstrate a photonic scheme for combinatorial optimization in analogy with adiabatic quantum algorithms and enforced by optical vector-matrix multiplications and scalable photonic technology.Comment: 9 pages, 4 figure

The α+d→ 6Li+γ\alpha + d \rightarrow ~ ^6\mathrm{Li} + \gamma astrophysical SS-factor and its implications for Big Bang Nucleosynthesis

The \alpha+d\rightarrow\, ^6{\rm Li}+\gamma radiative capture is studied in order to predict the $^6$Li primordial abundance. Within a two-body framework, the $\alpha$ particle and the deuteron are considered the structureless constituents of $^6$Li. Five $\alpha+d$ potentials are used to solve the two-body problem: four of them are taken from the literature, only one having also a tensor component. A fifth model is here constructed in order to reproduce, besides the $^6$Li static properties as binding energy, magnetic dipole and electric quadrupole moments, also the $S$-state asymptotic normalization coefficient (ANC). The two-body bound and scattering problem is solved with different techniques, in order to minimize the numerical uncertainty of the present results. The long-wavelength approximation is used, and therefore only the electric dipole and quadrupole operators are retained. The astrophysical $S$-factor is found to be significantly sensitive to the ANC, but in all the cases in good agreement with the available experimental data. The theoretical uncertainty has been estimated of the order of few % when the potentials which reproduce the ANC are considered, but increases up to $\simeq 20$ % when all the five potential models are retained. The effect of this $S$-factor prediction on the $^6$Li primordial abundance is studied, using the public code PArthENoPE. For the five models considered here we find $^6{\rm Li}/$H$= (0.9 - 1.8) \times 10^{-14}$, with the baryon density parameter in the 3-$\sigma$ range of Planck 2015 analysis, $\Omega_b h^2= 0.02226 \pm 0.00023$.Comment: 26 pages, 9 figure

Implication of the proton-deuteron radiative capture for Big Bang Nucleosynthesis

The astrophysical $S$-factor for the radiative capture $d(p,\gamma)^3$He in the energy-range of interest for Big Bang Nucleosynthesis (BBN) is calculated using an {\it ab-initio} approach. The nuclear Hamiltonian retains both two- and three-nucleon interactions - the Argonne $v_{18}$ and the Urbana IX, respectively. Both one- and many-body contributions to the nuclear current operator are included. The former retain for the first time, besides the $1/m$ leading order contribution ($m$ is the nucleon mass), also the next-to-leading order term, proportional to $1/m^3$. The many-body currents are constructed in order to satisfy the current conservation relation with the adopted Hamiltonian model. The hyperspherical harmonics technique is applied to solve the $A=3$ bound and scattering states. A particular attention is used in this second case in order to obtain, in the energy range of BBN, an uncertainty on the astrophysical $S$-factor of the order or below $\sim$1 %. Then, in this energy range, the $S$-factor is found to be $\sim$10 % larger than the currently adopted values.Part of this increase (1-3 %) is due to the $1/m^3$ one-body operator, while the remaining is due to the new more accurate scattering wave functions. We have studied the implication of this new determination for the $d(p,\gamma)^3$He $S$-factor on deuterium primordial abundance. We find that the predicted theoretical value for $^2$H/H is in excellent agreement with its experimental determination, using the most recent determination of baryon density of Planck experiment, and with a standard number of relativistic degrees of freedom $N_{\rm eff}=3.046$ during primordial nucleosynthesis.Comment: 5 pages, 2 figures, submitted to Phys. Rev. Let

Multifractal structure and intermittence in the AE index time series

The conventional approach to magnetospheric dynamics has not provided until now a satisfactory description of the singular behaviour of magnetospheric substorms. In this paper we present a multifractal analysis of AE time series, based on singularity analysis, a new tool to investigate signal dynamics features. The existence of a multifractal structure of the AE index with respect to time dilation has been investigated. The resulting multifractal behaviour of the signal can be interpreted as the signature of an underlying intermittence phenomenon. The derived singularity spectrum is well in agreement with the one of a two-scale Cantor model (P-model), a pure multiplicative model. The presence of intermittence in AE might indicate the occurrence of turbulence in magnetospheric dissipation processes

Astrophysical implications of the proton-proton cross section updates

The p(p,e^+ \nu_e)^2H reaction rate is an essential ingredient for theoretical computations of stellar models. In the past several values of the corresponding S-factor have been made available by different authors. Prompted by a recent evaluation of S(E), we analysed the effect of the adoption of different proton-proton reaction rates on stellar models, focusing, in particular, on the age of mid and old stellar clusters (1-12 Gyr) and on standard solar model predictions. By comparing different widely adopted p(p,e^+ \nu_e)^2H reaction rates, we found a maximum difference in the temperature regimes typical of main sequence hydrogen-burning stars (5x10^6 - 3x10^7 K) of about 3%. Such a variation translates into a change of cluster age determination lower than 1%. A slightly larger effect is observed in the predicted solar neutrino fluxes with a maximum difference, in the worst case, of about 8%. Finally we also notice that the uncertainty evaluation of the present proton-proton rate is at the level of few \permil, thus the p(p,e^+ \nu_e)^2H reaction rate does not constitute anymore a significant uncertainty source in stellar models.Comment: accepte