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Combining Neural Networks and Signed Particles to Simulate Quantum Systems More Efficiently

机译：结合神经网络和有符号粒子模拟量子力学   系统更有效率

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Recently a new formulation of quantum mechanics has been suggested whichdescribes systems by means of ensembles of classical particles provided with asign. This novel approach mainly consists of two steps: the computation of theWigner kernel, a multi-dimensional function describing the effects of thepotential over the system, and the field-less evolution of the particles whicheventually create new signed particles in the process. Although this method hasproved to be extremely advantageous in terms of computational resources - as amatter of fact it is able to simulate in a time-dependent fashion many- bodysystems on relatively small machines - the Wigner kernel can represent thebottleneck of simulations of certain systems. Moreover, storing the kernel canbe another issue as the amount of memory needed is cursed by the dimensionalityof the system. In this work, we introduce a new technique which drasticallyreduces the computation time and memory requirement to simulate time-dependentquantum systems which is based on the use of an appropriately tailored neuralnetwork combined with the signed particle formalism. In particular, thesuggested neural network is able to compute efficiently and reliably the Wignerkernel without any training as its entire set of weights and biases isspecified by analytical formulas. As a consequence, the amount of memory forquantum simulations radically drops since the kernel does not need to be storedanymore as it is now computed by the neural network itself, only on the cellsof the (discretized) phase-space which are occupied by particles. As its isclearly shown in the final part of this paper, not only this novel approachdrastically reduces the computational time, it also remains accurate. Theauthor believes this work opens the way towards effective design of quantumdevices, with incredible practical implications.
机译：最近，提出了一种新的量子力学公式，该公式通过带有标志的经典粒子的集合来描述系统。这种新颖的方法主要包括两个步骤：维格纳核的计算，描述电位对系统的影响的多维函数以及粒子的无场演化，最终在该过程中创建了新的带符号粒子。尽管已证明该方法在计算资源方面极为有利-实际上，它能够在相对较小的机器上以时间相关的方式对多个系统进行仿真，但Wigner内核可以代表某些系统的仿真瓶颈。此外，存储内核可能是另一个问题，因为所需的内存量会因系统的维数而减少。在这项工作中，我们引入了一种新技术，该技术大大减少了计算时间和内存需求，以模拟与时间相关的量子系统，该技术基于使用经过适当剪裁的神经网络和有符号粒子形式主义相结合。尤其是，建议的神经网络无需经过任何培训即可高效可靠地计算维格纳尔核，因为其整个权重和偏差集均由解析公式指定。结果，用于量子模拟的存储器的数量从根本上减少了，因为不再需要存储内核，因为它现在是由神经网络本身计算的，仅在（离散的）相空间的细胞上被粒子占据。正如本文最后部分清楚显示的那样，这种新颖的方法不仅大大减少了计算时间，而且仍然保持准确。作者认为，这项工作为实现量子器件的有效设计开辟了道路，具有不可思议的实际意义。

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    Sellier, Jean Michel;

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