Bridging the reality gap in quantum devices with physics-aware machine learning

TL;DR

This work bridges the reality gap using physics-aware machine learning, in particular, using an approach combining a physical model, deep learning, Gaussian random field, and Bayesian inference to infer the disorder potential of a nanoscale electronic device from electron transport data.

Abstract

The discrepancies between reality and simulation impede the optimisation and scalability of solid-state quantum devices. Disorder induced by the unpredictable distribution of material defects is one of the major contributions to the reality gap. We bridge this gap using physics-aware machine learning, in particular, using an approach combining a physical model, deep learning, Gaussian random field, and Bayesian inference. This approach has enabled us to infer the disorder potential of a nanoscale electronic device from electron transport data. This inference is validated by verifying the algorithm's predictions about the gate voltage values required for a laterally-defined quantum dot device in AlGaAs/GaAs to produce current features corresponding to a double quantum dot regime.

Figures (11)

• Figure 1: (a) Device geometry including the gate electrodes (labelled G1-G8), donor ion plane, and an example disorder potential experienced by confined electrons. Typical flow of current from source to drain is indicated by the white arrow. (b) Schematic of the disorder inference process. Colours indicate the following; red for experimentally controllable variables, green for quantities relevant to the electrostatic model, blue for experimental device, and yellow for machine learning methods. Dashed arrows represent the process of generating training data for the deep learning approximation and are not part of the disorder inference process.
• Figure 2: An example of the device model as discussed in Section \ref{['sec:device']}. Spatial coordinates $x$ and $y$ are used to indicate the scale of the device. (a) Electrostatic potential from the gate electrodes $\phi_{\mathrm{g}}$, (b) a disorder potential $\phi_{\mathrm{d}}$, and (c) self-consistent potential $\phi_{\mathrm{tot}}$ given the potentials in (a) and (b). (d) The electron density in the 2DEG given the potential in (c), which shows a single dot. (e) Example of MST path from source to drain in 2D (yellow line) with the location of $U^*$ is marked by a green circle. (f) The potential energy, $U$, corresponding to the MST path in (e) with $U^*$ marked by a green circle. The horizontal axis indicates the total distance moved in 2D space. The channel is closed since the value of $U^*$ is above the Fermi level indicated by the red dashed line.
• Figure 3: Gate architecture overlaid with inducing point locations $X$, indicated by blue dots (a) before optimisation and (b) after optimisation. Red circles indicate the two corners defining the rectangular array of inducing points. The location of these corners are optimised to ensure that the disorder potential values at the inducing points determines whether the transport channel is open or closed. Hence the optimised inducing points are located closer to the source and drain reservoirs.
• Figure 4: Disorder inference results using experimental data for three thermal cycles (A,B,C) of the same device. The inducing point locations, $Z_\mathrm{opt}$, are indicated by circles with the gate structure in the background. The colour of each inducing point represents the standard deviation over posterior samples of the disorder potential value at that point.
• Figure 5: (a) Predicting double dot locations. A unit vector $\mathbf{u}$ is passed to the filter which determines whether the vector is considered for the test device (which can be a real or simulated device). The filter uses the dot classifier $\mathcal{F}_D$ to scan along $\mathbf{v}=\mathrm{R}\mathbf{u}$ for each of the $n_\mathrm{s}$ disorder samples and the score is increased for each disorder sample which produces a double dot in the scan. Posterior disorder samples from the inference algorithm are shown. Vectors with a score greater than $n_\mathrm{s}/3$ are accepted to be tested. An example current trace (solid blue line) of a voltage vector from the origin to the limit of device operation is shown. The dashed red line indicates the $80\%$ threshold used to begin 2D current scans over gates G3 and G7. The 2D scans are taken at intervals along the original current trace (indicated by red circles). The resulting 2D current scans are passed to multiple human experts to label the presence of double quantum dots. (b) Example current scans over G3 and G7 which scored highly for double dots when labelled by 6 human experts for 3 different unit vectors. Each scan is a 200mV$\times$200mV window with the voltages associated with the direction of $\mathbf{u}$ at the centre.