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Combining neural networks and signed particles to simulate quantum systems more efficiently

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  • Sellier, Jean Michel

Abstract

Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner kernel, a multi-dimensional function describing the effects of the potential over the system, and the field-less evolution of the particles which eventually create new signed particles in the process. Although this method has proved to be extremely advantageous in terms of computational resources – as a matter of fact it is able to simulate in a time-dependent fashion many-body systems on relatively small machines – the Wigner kernel can represent the bottleneck of simulations of certain systems. Moreover, storing the kernel can be another issue as the amount of memory needed is cursed by the dimensionality of the system. In this work, we introduce a new technique which drastically reduces the computation time and memory requirement to simulate time-dependent quantum systems which is based on the use of an appropriately tailored neural network combined with the signed particle formalism. In particular, the suggested neural network is able to compute efficiently and reliably the Wigner kernel without any training as its entire set of weights and biases is specified by analytical formulas. As a consequence, the amount of memory for quantum simulations radically drops since the kernel does not need to be stored anymore as it is now computed by the neural network itself, only on the cells of the (discretized) phase-space which are occupied by particles. As its is clearly shown in the final part of this paper, not only this novel approach drastically reduces the computational time, it also remains accurate. The author believes this work opens the way towards effective design of quantum devices, with incredible practical implications.

Suggested Citation

  • Sellier, Jean Michel, 2018. "Combining neural networks and signed particles to simulate quantum systems more efficiently," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 62-71.
  • Handle: RePEc:eee:phsmap:v:496:y:2018:i:c:p:62-71
    DOI: 10.1016/j.physa.2017.12.122
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    References listed on IDEAS

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    1. Guilherme Tosi & Fahd A. Mohiyaddin & Vivien Schmitt & Stefanie Tenberg & Rajib Rahman & Gerhard Klimeck & Andrea Morello, 2017. "Silicon quantum processor with robust long-distance qubit couplings," Nature Communications, Nature, vol. 8(1), pages 1-11, December.
    2. B. E. Kane, 1998. "A silicon-based nuclear spin quantum computer," Nature, Nature, vol. 393(6681), pages 133-137, May.
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    Cited by:

    1. Hemmat Esfe, Mohammad & Kamyab, Mohammad Hassan & Afrand, Masoud & Amiri, Mahmoud Kiannejad, 2018. "Using artificial neural network for investigating of concurrent effects of multi-walled carbon nanotubes and alumina nanoparticles on the viscosity of 10W-40 engine oil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 610-624.

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