AI-enhanced tuning of quantum dot Hamiltonians toward Majorana modes

TL;DR

The paper tackles the challenge of robustly realizing Majorana zero modes in a quantum-dot chain by introducing PINNAT, an unsupervised, physics-informed autotuning framework that learns from conductance maps and uses a differentiable Majorana metric $\mathcal{M}$ to predict parameter updates. A vision-transformer ingests transport maps $G(H(P))$ and outputs $\delta P$ to steer the Hamiltonian toward the topological regime, enabling both single-step corrections and iterative refinement. Results show that PINNAT can enhance $\mathcal{M}$ and realize edge-localized, near-zero-energy states, with global tuning (e.g., $V_Z$) often more effective than local tuning (e.g., $\mu_n$) and with partial generalization beyond the training range. The framework merges quantum transport simulations with physics-informed ML to enable autonomous tuning in noisy mesoscopic systems and scales to longer Majorana-supporting chains.

Abstract

We propose a neural network-based model capable of learning the broad landscape of working regimes in quantum dot simulators, and using this knowledge to autotune these devices - based on transport measurements - toward obtaining Majorana modes in the structure. The model is trained in an unsupervised manner on synthetic data in the form of conductance maps, using a physics-informed loss that incorporates key properties of Majorana zero modes. We show that, with appropriate training, a deep vision-transformer network can efficiently memorize relation between Hamiltonian parameters and structures on conductance maps and use it to propose parameters update for a quantum dot chain that drive the system toward topological phase. Starting from a broad range of initial detunings in parameter space, a single update step is sufficient to generate nontrivial zero modes. Moreover, by enabling an iterative tuning procedure - where the system acquires updated conductance maps at each step - we demonstrate that the method can address a much larger region of the parameter space.

Figures (6)

• Figure 1: Scheme of the QDs-based KC-simulator autotuning system (PINNAT). Black (blue) arrows show the system training (inference) path. Vision transformer model is fed with conductance maps to predict parameter corrections, that should decrease $\mathcal{M}$-based loss function, simultaneously increasing the probability of MZMs emergence.
• Figure 2: $\mathcal{M}$ metric map for uniform (across the dots) change of different parameters -- resulting in shifted $P$ -- for (b) model adjusting $\{\mu_n, t_n, \lambda_n\}$, and (c) adjusting $\{\mu_n, V_\mathrm{Z}\}$. The ranges of the parameter sampling that were used in the model training set are marked with a gray rectangle. The reference parameter values $P_0$ are marked with a red dot. In (a), we present values of $\mathcal{M}(H(P))$ before parameter tuning, while in (b) and (c) $\mathcal{M}(H(P+\delta P))$ -- after tuning.
• Figure 3: Same as in Fig. \ref{['fig:m_map_total']}: $\mathcal{M}$ metric maps (a) before, and (b,c) after parameters tuning, but now for local shift of selected pair of parameters.
• Figure 4: Iterative autotuning procedure for (a) model adjusting $\{\mu_n, t_n, \lambda_n\}$, and (b) adjusting $\{\mu_n, V_\mathrm{Z}\}$. In the first (left) plot, we present $\mathcal{M}$ map before tuning. Then, in the center, parameters are tuned with a single step of NN corrections. Finally, in the last (right) plot, there is a map plotted for parameters tuned within 10 subsequent steps of NN corrections.
• Figure 5: Three-QD chain Hamiltonian $H$ as a function of the offset $\mu$ added to local potentials: $\mu_n\rightarrow\mu_n+\mu-0.6$ meV (dashed vertical line marks the reference $\mu=0.6\,\mathrm{meV}$). Additionally $\mathcal{M}$ metric is plotted, and eigenvalues are colored (left column) with edge occupations -- 1 means that the state is localized on the edges, while 0 means that state is localized in the center dot, or (right column) electron-hole symmetry -- calculated as difference between density of electrons and holes. Plots are presented for (a) reference parameters; (b) modified $\lambda_1$ and $\lambda_2$; (c) parameters from (b) but with NN-tuned $\{\mu_n, t_n, \lambda_n\}$; (d) parameters from (b) with NN-tuned $\{\mu_n, V_\mathrm{Z}\}$.