Forming complex neurons by four-wave mixing in a Bose-Einstein condensate
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929222968147968 |
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| author | Hansmann, Kai Niklas Walser, Reinhold |
| author_facet | Hansmann, Kai Niklas Walser, Reinhold |
| contents | A physical artificial complex-valued neuron is formed by four-wave mixing in a homogeneous three-dimensional Bose-Einstein condensate. Bragg beamsplitter pulses prepare superpositions of three plane-waves states as an input- and the fourth wave as an output signal. The nonlinear dynamics of the non-degenerate four-wave mixing process leads to Josephson-like oscillations within the closed four-dimensional subspace and defines the activation function of a neuron. Due to the high number of symmetries, closed form solutions can be found by quadrature and agree with numerical simulation. The ideal behaviour of an isolated four-wave mixing setup is compared to a situation with additional population of rogue states. We observe a robust persistence of the main oscillation. As an application for neural learning of this physical system, we train it on the XOR problem. After $100$ training epochs, the neuron responds to input data correctly at the $10^{-5}$ error level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16302 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Forming complex neurons by four-wave mixing in a Bose-Einstein condensate Hansmann, Kai Niklas Walser, Reinhold Quantum Gases Disordered Systems and Neural Networks A physical artificial complex-valued neuron is formed by four-wave mixing in a homogeneous three-dimensional Bose-Einstein condensate. Bragg beamsplitter pulses prepare superpositions of three plane-waves states as an input- and the fourth wave as an output signal. The nonlinear dynamics of the non-degenerate four-wave mixing process leads to Josephson-like oscillations within the closed four-dimensional subspace and defines the activation function of a neuron. Due to the high number of symmetries, closed form solutions can be found by quadrature and agree with numerical simulation. The ideal behaviour of an isolated four-wave mixing setup is compared to a situation with additional population of rogue states. We observe a robust persistence of the main oscillation. As an application for neural learning of this physical system, we train it on the XOR problem. After $100$ training epochs, the neuron responds to input data correctly at the $10^{-5}$ error level. |
| title | Forming complex neurons by four-wave mixing in a Bose-Einstein condensate |
| topic | Quantum Gases Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2309.16302 |