[Paper Review] Cross-Platform Autonomous Control of Minimal Kitaev Chains

David van Driel, Rouven Koch+22 more|arXiv (Cornell University)|May 7, 2024

Mobile Agent-Based Network Management4 citations

TL;DR

This paper presents a cross-platform transfer learning approach using a convolutional neural network (CNN) to autonomously tune minimal Kitaev chains to Majorana zero mode sweet spots. By training on a theoretical model and fine-tuning on a 2D electron gas platform, the method successfully locates Majorana sweet spots in a 1D nanowire quantum dot device with 67.6% accuracy within ±1.5 mV, demonstrating transferable, data-efficient quantum control across experimental platforms.

ABSTRACT

Contemporary quantum devices are reaching new limits in size and complexity, allowing for the experimental exploration of emergent quantum modes. However, this increased complexity introduces significant challenges in device tuning and control. Here, we demonstrate autonomous tuning of emergent Majorana zero modes in a minimal realization of a Kitaev chain. We achieve this task using cross-platform transfer learning. First, we train a tuning model on a theory model. Next, we retrain it using a Kitaev chain realization in a two-dimensional electron gas. Finally, we apply this model to tune a Kitaev chain realized in quantum dots coupled through a semiconductor-superconductor section in a one-dimensional nanowire. Utilizing a convolutional neural network, we predict the tunneling and Cooper pair splitting rates from differential conductance measurements, employing these predictions to adjust the electrochemical potential to a Majorana sweet spot. The algorithm successfully converges to the immediate vicinity of a sweet spot (within 1.5 mV in 67.6% of attempts and within 4.5 mV in 80.9% of cases), typically finding a sweet spot in 45 minutes or less. This advancement is a stepping stone towards autonomous tuning of emergent modes in interacting systems, and towards foundational tuning machine learning models that can be deployed across a range of experimental platforms.

Motivation & Objective

• Address the challenge of autonomous tuning in complex quantum devices with high-dimensional parameter spaces.
• Overcome the limitation of platform-specific tuning by enabling transfer learning across distinct experimental platforms (theory, 2D electron gas, 1D nanowire).
• Develop a machine learning framework that generalizes across platforms without requiring direct experimental data from the target device.
• Achieve autonomous convergence to Majorana zero mode sweet spots using only differential conductance measurements.
• Demonstrate a scalable, data-efficient approach for tuning emergent topological modes in interacting quantum systems.

Proposed method

• Train a convolutional neural network (CNN) on a theoretical Kitaev chain model to classify the dominant tunneling process (elastic co-tunneling vs. crossed-Andreev reflection).
• Use the CNN output to estimate the ratio $(t - \Delta)/(t + \Delta)$, where $t$ is tunneling amplitude and $\Delta$ is superconducting pairing, to identify the Majorana sweet spot.
• Apply a gradient descent algorithm that adjusts the hybrid plunger gate voltage ($V_{\text{ABS}}$) based on real-time differential conductance measurements.
• Implement a learning rate annealing strategy with momentum and adaptive step size control to improve convergence stability.
• Use a tolerance threshold $\tau = \frac{1}{32} \left( \frac{\gamma}{\Delta^*} \right)^2$ to define convergence, where $\gamma$ is resonance linewidth and $\Delta^*$ is the target gap.
• Log and detect overshoots during tuning to dynamically adjust learning rate and direction, improving robustness in non-ideal conditions.

Figure 1: Device A set-up and characterization. a. False color SEM micrograph of our device, and the circuit. An InSb nanowire (green) is contacted by a grounded Al shell (blue) and two normal leads (yellow). The nanowire is placed on bottom gates (red). The relevant gate voltages are indicated by t

Experimental results

Research questions

• RQ1 Can a machine learning model trained on a theoretical Kitaev chain model be effectively fine-tuned on experimental data from a different platform (2D electron gas) and then deployed to tune a distinct experimental realization (1D nanowire)?
• RQ2 To what extent can a CNN-based classifier of tunneling processes generalize across vastly different experimental platforms with varying many-body interactions and measurement noise?
• RQ3 What is the convergence performance of the autonomous tuning algorithm in locating Majorana zero mode sweet spots in a real 1D nanowire quantum dot device?
• RQ4 How does the algorithm perform in the presence of measurement noise and limited training data, particularly when the target platform differs from the training platforms?
• RQ5 Can the algorithm be made robust to poor initial predictions by incorporating adaptive learning rate and overshoot detection mechanisms?

Key findings

• The algorithm successfully converged to within ±1.5 mV of the known Majorana sweet spot in 67.6% of tuning attempts on the 1D nanowire device.
• In 80.9% of cases, the algorithm reached within ±4.5 mV of the sweet spot, demonstrating strong robustness and reliability.
• The average tuning time to convergence was 45 minutes or less, indicating practical feasibility for integration into experimental workflows.
• The CNN-based classification of tunneling processes enabled accurate estimation of the $(t - \Delta)/(t + \Delta)$ ratio, which is critical for identifying the sweet spot.
• The method achieved cross-platform transfer learning: model trained on theory, fine-tuned on 2D electron gas data, and applied to 1D nanowire device without direct data from the target platform.
• An unconverged run highlighted limitations in CNN generalization at low $t + \Delta$ values, suggesting a need for improved data coverage in weak-coupling regimes.

Figure 2: Device B charge stability diagrams and simulations. a. Schematic overview of the model system. Two quantum dots (QDs) are coupled by an Andreev bound state (ABS) in a semiconductor (gray) coupled to a grounded superconductor (blue). b. False color SEM image of device B. A 1D channel is def