Speaker
Description
Machine learning (ML) methods have shown great potential in tackling challenging problems within condensed matter physics and quantum many-body systems. In this talk, I will present recent developments from our research on leveraging deep learning (DL) techniques to reconstruct the effective Hamiltonian of quantum dot (QD) arrays from transport measurements, particularly focusing on conductance maps as a function of gate voltages.
QDs defined by electrostatic gating, which host individual electrons or holes, are promising candidates for scalable quantum computing and quantum simulator platforms. A particularly compelling application involves simulating minimal Kitaev chain models [1], which host so-called poor man's Majorana modes [2]. Accurately identifying (or autotuning) the Hamiltonian parameters of these systems from experimental data remains a significant challenge [4-5].
Our proposed approach employs a physics-informed autoencoder architecture consisting of a deep residual convolutional neural network (e.g. ResNet) or Vision Transformer encoder to predict the QD Hamiltonian parameters. The decoder is a differentiable module (implemented in PyTorch) employing an analytical Green’s function formalism to calculate conductance from these predicted parameters. The entire system is trained end-to-end, optimizing the reconstruction of the input conductance maps.
Embedding physical principles directly within the neural network (NN), using technique we previously developed [6], facilitates physically meaningful predictions and efficient generalization. The method represents a step forward in geometric DL, explicitly integrating physical constraints into the NN architecture, and provides a powerful framework for experimentally relevant Hamiltonian reconstruction in quantum simulation platforms.
[1] M. Leijnse and K. Flensberg, Phys. Rev. B 86, 134528 (2012).
[2] G. Dvir et al., Nature 614, 445 (2023).
[3] D. Koch et al., Phys. Rev. Appl. 20, 044081 (2023).
[4] J. Wang et al., Nature Physics 13, 551 (2017).
[5] V. Gebhart et al., Nature Reviews Physics 5, 141 (2023).
[6] M. Krawczyk et al., Phys. Rev. A 109, 022405 (2024).
