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Learning Hamiltonians for solid-state quantum simulators

Jarosław Pawłowski, Mateusz Krawczyk

TL;DR

A generalizable framework for learning to identify effective Hamiltonians directly from experimental data in solid-state quantum systems, based on a physics-informed neural network architecture that embeds physical constraints directly into the model structure.

Abstract

We introduce a generalizable framework for learning to identify effective Hamiltonians directly from experimental data in solid-state quantum systems. Our approach is based on a physics-informed neural network architecture that embeds physical constraints directly into the model structure. Unlike purely data-driven supervised schemes, the proposed unsupervised autoencoder-based method incorporates the governing physics (here, the S-matrix formalism) within the decoder network, ensuring that the learned representations remain physically meaningful. Through numerical learning experiments, we demonstrate automated characterization of programmable solid-state simulators from transport measurements, exemplified by a triple quantum dot chain. The trained model generalizes beyond the training domain and accurately infers Hamiltonian parameters from transport data. While the model has finite capacity -- leading to degraded performance when the parameter space becomes excessively large or structurally diverse -- we identify regimes in which robust generalization is maintained. We further show how to train the model to handle noisy measurements, reflecting realistic experimental conditions.

Learning Hamiltonians for solid-state quantum simulators

TL;DR

A generalizable framework for learning to identify effective Hamiltonians directly from experimental data in solid-state quantum systems, based on a physics-informed neural network architecture that embeds physical constraints directly into the model structure.

Abstract

We introduce a generalizable framework for learning to identify effective Hamiltonians directly from experimental data in solid-state quantum systems. Our approach is based on a physics-informed neural network architecture that embeds physical constraints directly into the model structure. Unlike purely data-driven supervised schemes, the proposed unsupervised autoencoder-based method incorporates the governing physics (here, the S-matrix formalism) within the decoder network, ensuring that the learned representations remain physically meaningful. Through numerical learning experiments, we demonstrate automated characterization of programmable solid-state simulators from transport measurements, exemplified by a triple quantum dot chain. The trained model generalizes beyond the training domain and accurately infers Hamiltonian parameters from transport data. While the model has finite capacity -- leading to degraded performance when the parameter space becomes excessively large or structurally diverse -- we identify regimes in which robust generalization is maintained. We further show how to train the model to handle noisy measurements, reflecting realistic experimental conditions.
Paper Structure (1 section, 5 equations, 6 figures)

This paper contains 1 section, 5 equations, 6 figures.

Table of Contents

  1. Acknowledgments

Figures (6)

  • Figure 1: (a) Chain of the Rashba QDs. (b) Proposed HL architecture composed of encoder---predictor and physics-decoder.
  • Figure 2: Rashba chain of QDs proximitized by an $s$-wave superconductor. Top row: eigenstates as a function of voltage offset with colors encoding: (a,b) edges ($L$ and $R$ dot) occupation, (c) electron-hole symmetry. Reference parameters configuration $P_0$, giving MZM-like states, is marked by orange arrow. Bottom row: conductance maps as a function of (d) voltage applied to the left dot, (e) voltage on the center dot, and (f) the Zeeman field.
  • Figure 3: Results for the HL of the Rashba chain, Eq. \ref{['eq:qds']}, of three quantum dots proximitized by an $s$-wave superconductor. Top row (a-c): error for the conductance maps reconstruction (via the predicted parameters) as a function of parameter variations---the white box denotes the region where training data was sampled. Middle (d,e) and bottom (f,g) rows: example input and predicted conductance maps (shown as middle/bottom pairs) for various parameter configurations indicated by the respective symbols. The default configuration that yields MZMs is marked with an orange circle
  • Figure 4: HL results for a smaller training range, denoted by white boxes on the conductance reconstruction error maps (a-c) within the parameter space. Two specific $G$ reconstruction cases (d,e) are indicated in the parameter space by a red square in (b) and a blue triangle in (c), respectively.
  • Figure 5: HL results for a larger training range, indicated by wider white boxes on the conductance reconstruction error maps (a-c). In this case, 50k training samples were used.
  • ...and 1 more figures