Large Scale Optimization of Disordered Hubbard Models through Tensor and Neural Networks

TL;DR

This paper presents a neural network-based method using tensor-network data to efficiently tune large disordered quantum-dot arrays for spin qubit platforms, avoiding complex ground state calculations.

Contribution

It introduces a sliding-window approach with neural networks trained on tensor data to accurately predict local disorder parameters in large 2D quantum-dot arrays.

Findings

High fidelity prediction of on-site disorder with R^2 > 0.99 in 3x3 arrays

Retains high accuracy (R^2 ≈ 0.98) after fine-tuning on larger samples

Robust prediction of disorder parameters even in fully disordered 5x5 arrays

Abstract

We theoretically demonstrate a practical method for tuning randomly disordered 2D quantum-dot grids underlying spin qubit platforms using vision-based neural networks trained on tensor-network generated charge-stability data. We show that a simulatable local $3\times 3$ window already contains sufficient information to tune the central dot within a much larger array, thereby validating a sliding-window approach in which one tunes a local region and then translates that window across the lattice to calibrate a larger device. This avoids the computationally intractable necessity for obtaining the ground states for large systems with exponentially large Hilbert space. For the experimentally relevant case where only the on-site disorder is unknown, the neural network predicts the relevant parameters with very high fidelity in the $3\times 3$ setting [$R^2 >0.99$], and after fine tuning on only a small number of larger-device samples, it retains high accuracy for the central dot of a $5\times 5$ plaquette [$R^2\approx 0.98$]. When all the dots parameters are treated as unknown, prediction of the on-site disorder remains robust [$R^2>0.9$ for both $3\times 3$ and $5\times 5$], although the remaining parameters are substantially more difficult to infer from the same charge-stability data. This shows that the most practically important disorder parameter for tuning can still be inferred reliably even in the fully disordered setting for the computationally difficult 5x5 arrays.