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Abstract Training of neural networks (NNs) has emerged as a major consumer of both computational and energy resources. Quantum computers were coined as a root to facilitate training, but no experimental evidence has been presented so far. Here we demonstrate that quantum annealing platforms, such as D-Wave, can enable fast and efficient training of classical NNs, which are then deployable on conventional hardware. From a physics perspective, NN training can be viewed as a dynamical phase transition: the system evolves from an initial spin glass state to a highly ordered, trained state. This process involves eliminating numerous undesired minima in its energy landscape. The advantage of annealing devices is their ability to rapidly find multiple deep states. We found that this quantum training achieves superior performance scaling compared to classical backpropagation methods, with a clearly higher scaling exponent (1.01 vs. 0.78). It may be further increased up to a factor of 2 with a fully coherent quantum platform using a variant of the Grover algorithm. Furthermore, we argue that even a modestly sized annealer can be beneficial to train a deep NN by being applied sequentially to a few layers at a time. 

Finding an exact ground state of a three-dimensional (3D) Ising spin glass is proven to be an NP-hard problem (i.e., at least as hard as any problem in the nondeterministic polynomial-time (NP) class). Given validity of the exponential time hypothesis, its computational complexity was proven to be no less than $2^{N^{2/3}}$, where $N$is the total number of spins. Here, we report results of extensive experimentation with D-Wave 3D annealer with $N\le 5627$. We found exact ground states (in a probabilistic sense) for typical realizations of 3D spin glasses with the efficiency, which scales as $2^{N/\beta }$with $\beta \approx {10}^3$. Based on statistical analysis of low-energy states, we argue that with an improvement of annealing protocols and device noise reduction, $\beta$can be increased even further. This suggests that, for $N<{\beta }^3$, annealing devices provide most efficient way to find an exact ground state. 

A<sc>bstract</sc> In this paper, we propose a construction of GLSM defects corresponding to Schubert cycles in Lagrangian Grassmannians, following recent work of Closset-Khlaif on Schubert cycles in ordinary Grassmannians. In the case of Lagrangian Grassmannians, there are superpotential terms in both the bulk GLSM as well as on the defect itself, enforcing isotropy constraints. We check our construction by comparing the locus on which the GLSM defect is supported to mathematical descriptions, checking dimensions, and perhaps most importantly, comparing defect indices to known and expected polynomial invariants of the Schubert cycles in quantum cohomology and quantum K theory. 

In this Letter, we introduce FusionNet, a multi-modality deep learning framework designed to predict and analyze output pulses in high-power rare-earth-doped laser systems driving parametric conversion in homogeneous guided nonlinear media. FusionNet integrates temporal, spectral, and physical experimental conditions to model ultrafast nonlinear phenomena, including parametric nonlinear frequency conversion, self-phase modulation, and cross-phase modulation in homogeneous guided systems such as gas-filled hollow-core fibers. These systems bridge physical models with experimental data, advancing our understanding of light-guiding principles and nonlinear interactions while expediting the design and optimization of on-demand high-power, high-brightness systems. Our results demonstrate a 73% reduction in prediction error and an 83% improvement in computational efficiency compared to conventional neural networks. This work establishes a new paradigm for accelerating parametric simulations and optimizing experimental designs in high-power laser systems, with further implications for high-precision spectroscopy, quantum information science, and distributed entangled interconnects. 

Abstract Quantum computers promise a qualitative speedup in solving a broad spectrum of practical optimization problems. The latter can be mapped onto the task of finding low-energy states of spin glasses, which is known to be exceedingly difficult. Using D-Wave’s 5000-qubit quantum processor, we demonstrate that a recently proposed iterative cyclic quantum annealing algorithm can find deep low-energy states in record time. We also find intricate structures in a low-energy landscape of spin glasses, such as a power-law distribution of connected clusters with a small surface energy. These observations offer guidance for further improvement of the optimization algorithms. 

Lightwave pulse shaping in the picosecond regime has remained unaddressed because it resides beyond the limits of state-of-the-art techniques, due to either its inherently narrow spectral content or fundamental speed limitations in electronic devices. The so-called picosecond shaping gap hampers progress in all areas correlated with time-modulated light–matter interactions, such as photoelectronics, health and medical technologies, and energy and materials sciences. We report on a novel nonlinear method to simultaneously frequency-convert and adaptably shape the envelope of light wave packets in the picosecond regime by balancing spectral engineering and nonlinear conversion in solid-state nonlinear media, without requiring active devices. We capture computationally the versatility of this methodology across a diverse set of nonlinear conversion chains and initial conditions. We also provide experimental evidence of this framework producing picosecond-shaped, ultranarrowband, near-transform-limited light pulses from broadband, femtosecond input pulses, paving the way toward programmable lightwave shaping at gigahertz-to-terahertz frequencies.