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Abstract Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as$${{{{{{{\mathcal{O}}}}}}}}({T}^{2}\times {{{{{{{\rm{polylog}}}}}}}}(n))$$ $O\left(T^2\times \mathrm{polylog}\left(n\right)\right)$, wherenis the size of the models andTis the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems. 

The cratonic lithosphere is a vast host for deep recycled carbon, trapping up to several weight percent CO₂ at depths overlapping the seismic mid-lithospheric discontinuities (MLDs). However, the role of carbonates, especially for the latest discovered amorphous calcium carbonate (CaCO₃), is underestimated in the formation of MLDs. Using the pulse-echo-overlap method in a Paris-Edinburgh press coupled with synchrotron X-ray diffraction, we explored the acoustic velocities of CaCO₃ under high pressure-temperature (P-T) conditions relevant to the cratonic lithosphere. Two anomalous velocity drops were observed associated with the phase transition from aragonite to amorphous phase and with the pressure-induced velocity drop in the amorphous phase around 3 GPa, respectively. Both drops are comparable with approximately 35% and 52% reductions for compressional (V_P) and shear (V_S) wave velocities, respectively. The V_P and V_S values of the amorphous CaCO₃ above 3 GPa are about 1/2 and 1/3 of those of the major upper-mantle minerals, respectively. These velocity reductions caused by the presence of CaCO₃ would readily cause MLDs at depths of 70–120 km dependent on the geotherm even if only 1–2 vol.% CaCO₃ is present in the cratonic lithosphere. 

Fe2O3 is an appealing anode material due to its high specific capacity (1007 mAh g− 1), low cost, natural abundance, and nontoxicity. However, its unstable structure during cycling processes has hindered its potential. In this study, we present a “green” synthesis method to fabricate stable porous Fe2O3 encapsulated in a buffering hollow structure (p-Fe2O3@h-TiO2) as an effective anode material for Li-ion batteries. The synthesis process only involves glucose as an “etching” agent, without the need for organic solvents or difficult-to-control environments. Characterizations of the nanostructures, chemical compositions, crystallizations, and thermal behaviors for the intermediate/final products confirm the formation of p-Fe2O3@h-TiO2. The synthesized Fe2O3 anode material effectively accommodates volume change, decreases pulverization, and alleviates agglomeration, leading to a high capacity that is over eleven times greater than that of the as-received commercial Fe2O3 after a long cycling process. This work provides an attractive, “green” and efficient method to convert commercially abundant resources like Fe2O3 into effective electrode materials for energy storage systems.