There is a growing pursuit to create neuromorphic devices that are able to perform machine learning tasks, both in an energy efficient manner and compatible with CMOS architecture. These approaches are based on taking the complex response of materials and mimicking aspects of a given machine learning model. Typically, what cannot be mimicked directly in a material, such as learning, is supplemented by other devices, circuitry, or external computers. These various approaches often face a number of bottlenecks, related to scaling, functionality independent of computers, and energy efficient operation. Ultimately constructing autonomous materials, namely individual materials that independently adapt their physical properties based on input data, requires deeper fundamental research linking physical processes to machine learning concepts. In this way, it is necessary to link quantum phenomena in materials to concepts like plasticity, memory, and learning. In this way, new types of quantum materials can be designed for autonomous recognition, as well as new functionalities can be explored, such as quantum machine learning. Energy-based models, like the Boltzmann machine, provide a natural link between physics and machine learning functionality via the Ising model and the physics of multi-well potentials and glasses (1, 2). I will discuss a new model system, based on the recently developed concept of orbital memory (3), which mimics the behavior of a Boltzmann machine directly in its stochastic dynamics and in one elemental material, down to the atomic-scale (4). Using scanning tunneling microscopy (STM) to fabricate nano-scale arrays of cobalt atoms on semiconducting black phosphorus, we observe stochastic noise described by the tunable multi-well landscapes seen in stochastic energy-based models. Utilizing a concept based on separation of time scales and the anisotropic behavior of black phosphorus (5), I will show that these multi-well landscapes are adaptive and exhibit inherently coupled neural and synaptic dynamics, at the atomic-scale. I will discuss perspectives of learning in these systems, and how such model systems provide fundamental insight into the future design of quantum-based brain-like devices. This work was done in collaboration with H.J. Kappen, Brian Kiraly, Elze J. Knol, and Werner M.J. van Weerdenburg. This work was funded by NWO-Vidi Manipulating the interplay between superconductivity and chiral magnetism at the single-atom level” with project number 680-47-534. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 818399).

**References:**

 1. A. Kolmus, M. I. Katsnelson, A. A. Khajetoorians and H. J. Kappen, New J. Phys. 22 (2), 023038 (2020). 2. U. Kamber, A. Bergman, A. Eich, D. Iusan, M. Steinbrecher, N. Hauptmann, L. Nordström, M. I. Katsnelson, D. Wegner, O. Eriksson and A. A. Khajetoorians, Science 368 (6494), eaay6757 (2020). 3. B. Kiraly, A. N. Rudenko, W. M. J. van Weerdenburg, D. Wegner, M. I. Katsnelson and A. A. Khajetoorians, Nat. Commun. 9 (1), 3904 (2018). 4. B. Kiraly, E. J. Knol, H. J. Kappen and A. A. Khajetoorians, arXiv, 2005.01547 (2020). 5. B. Kiraly, E. J. Knol, K. Volckaert, D. Biswas, A. N. Rudenko, D. A. Prishchenko, V. G. Mazurenko, M. I. Katsnelson, P. Hofmann, D. Wegner and A. A. Khajetoorians, Phys. Rev. Lett. 123 (21), 216403 (2019).

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 An atomic-scale Boltzmann machine capable of self-adaption

*Session Chair: Olga Kazakova, National Physical Laboratory*

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