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Machine Learning Techniques for Solving Quantum Many-Body Problems (QuanticLearn)
Results
Phase I (2021)
- Solving many-body problems. Bi-particle R-matrix formalism and applications of quantum information.
- Implementation of NEGF-DFT scheme for an atomistic description of nanoelectronic devices.
- Preliminary results concerning machine learning techniques.
- Scientific report -- Phase I (2021)
Phase II (2022)
Phase III (2023)
Brief summary of the results:
Designing nanodevices for quantum information transfer and processing requires a significant computational effort, as the interacting few-electron systems are described in the framework of quantum mechanics. Usually, many configurations need to be considered before an optimal design is reached and the diagonalizations of the many-body Hamiltonians becomes prohibitive. The machine learning (ML) techniques are able to bypass the time and resource consuming matrix diagonalizations and provide a rapid prediction of the targeted quantity for new instances, once the model is trained on the available computed data.
Within this project, we implemented a series of ML approaches like multivariate least squares (MLS), kernel ridge regression (KRR), Gaussian process regression (GPR) and artificial neural networks (ANNs) in order to find the eigenenergies of a few-electron system confined by top gate potentials. To this end we performed a multi-target regression and obtained accuracies (R2) of more than 0.96.
Perhaps one of the most interesting results of the project concerns the development of image-to-image translation techniques based on conditional generative-adversarial neural networks (cGANs) for mapping confinement potentials to the ground state charge densities. A cGAN includes two neural networks: the first one, called generator, produces output-images from input-images, while the second one classifies images into real (calculated) and fake (generated). The interaction between the two networks makes the generator produce better and better images, while the discriminator becomes more accurate in distinguishing real from fake. The model is updated using a training set until the generated images cannot be anymore distinguished from the real ones. Using this method we were able to efficiently and accurately describe the charge density in the ground state for new test systems, having as input the confinement potential, without diagonalizing the many-body Hamiltonian. This method was used also for the inverse problem, i.e. a mapping from a V-representable charge density to a potential map. This is highly important as, the inverse problem is typically much more difficult to solved and, in many cases, there is no obvious solution. Inverse design (of nanostructures) concerns finding the structure from desired physical properties or device functionalities and it is a very active field of research, which can be approached with the current methodology.
Also the working principles of prototypical devices like quantum sorters (QSs) and quantum neurons (QNs) have been investigated. Measuring the physical observable of a quantum state is not an easy task. The QS device identifies the quantum states from a sequence of incident states, which is important for the read-out of the quantum states that result in a quantum computation. On the other hand, neuromorphic structures were investigated and the possibility transfer the charge between the different terminal was investigated. A prototypical reconfigurable device was proposed and analyzed in the combined framework of exact diagonalization and cGAN ML approach. This lays the grounds for designing active circuit elements for quantum architectures.
The project also covered interesting topics concerning quantum communication and topological properties of Josephson junctions, as well as efficient NEGF-DFT-ML schemes for quantum transport. The tools developed here create the premises for advances in the field of quantum devices, material physics, while the large degree of generality of the ML techniques brings a huge potential to be employed in rather different fields of research.
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