Transfer Learning and the Early Estimation of Single-Photon Source Quality using Machine Learning Methods

TL;DR

This work investigates whether machine learning can accelerate the early estimation of single-photon source quality, quantified by $g^{(2)}(0)$, from incomplete two-photon coincidence histograms measured by Hanbury Brown–Twiss interferometry. Using eight FI-SEQUR datasets from an InGaAs/GaAs quantum dot, models are trained on seven laser-intensity contexts and tested on the eighth to probe transfer learning, comparing standard least-squares fitting to five ML predictors (three linear, two ensemble). The results show that, when tested within the same context, linear and ensemble ML can outperform the traditional fitting, but cross-context transfer remains uncertain and often inferior in the long run; synthetic data and adaptive transfer learning provide nuanced insights, suggesting that feature engineering and model adaptation may be required for robust generalization. Overall, ML holds promise for rapid early SPS-quality estimation, but its practical impact hinges on improving transferability across experimental contexts and designing informative features or adaptive strategies for SPS variability.

Abstract

The use of single-photon sources (SPSs) is central to numerous systems and devices proposed amidst a modern surge in quantum technology. However, manufacturing schemes remain imperfect, and single-photon emission purity must often be experimentally verified via interferometry. Such a process is typically slow and costly, which has motivated growing research into whether SPS quality can be more rapidly inferred from incomplete emission statistics. Hence, this study is a sequel to previous work that demonstrated significant uncertainty in the standard method of quality estimation, i.e. the least-squares fitting of a physically motivated function, and asks: can machine learning (ML) do better? The study leverages eight datasets obtained from measurements involving an exemplary quantum emitter, i.e. a single InGaAs/GaAs epitaxial quantum dot; these eight contexts predominantly vary in the intensity of the exciting laser. Specifically, via a form of `transfer learning', five ML models, three linear and two ensemble-based, are trained on data from seven of the contexts and tested on the eighth. Validation metrics quickly reveal that even a linear regressor can outperform standard fitting when it is tested on the same contexts it was trained on, but the success of transfer learning is less assured, even though statistical analysis, made possible by data augmentation, suggests its superiority as an early estimator. Accordingly, the study concludes by discussing future strategies for grappling with the problem of SPS context dissimilarity, e.g. feature engineering and model adaptation.

Figures (7)

• Figure 1: Example histograms for the 1p2uW (left column) and 30uW (right column) experimental contexts, where the raw time delay between triggered detectors denotes which bin of $0.256$ ns width a corresponding coincidence is assigned to. These are close-ups; the full $500$ ns domain contains $40$ peaks. Row 1: the first $10$ s snapshot of measurement. Row 2: the accumulation of ${\sim}1000$ detections. Row 3: the accumulation of ${\sim}10000$ detections. Row 4: the full duration of interferometry. Observations are overlaid with optimised fits of $R(\tau_i; \theta) \times t$. Units of $R_b$ and $R_p$ are Hz. Units of $1/\gamma_p$ are s. Estimate for $\tau_0$ quickly shifts from $61.4$ to $61.1$ ns between Row 1 and 4.
• Figure 2: Fitting and linear ML model estimates of $g$ for each FI-SEQUR dataset based on histograms of experimentally accumulated detections at every $10$ s timestep. The 'Fit' trace denotes estimates made by least-squares fitting, with the final value defining the ground truth for each dataset, i.e. a horizontal dashed 'Best' line. The ML models, trained on the other seven contexts prior to estimation, are: ordinary least squares (OLS), stochastic gradient descent (SGD), and partial least squares regression (PLSR). The measurement-time axis is logarithmic, and the first and second vertical dotted lines mark the times at which $1000$ and $10000$ detections are accumulated, respectively, per dataset.
• Figure 3: Fitting and ensemble ML model estimates of $g$ for each FI-SEQUR dataset based on histograms of experimentally accumulated detections at every $10$ s timestep. The 'Fit' trace denotes estimates made by least-squares fitting, with the final value defining the ground truth for each dataset, i.e. a horizontal dashed 'Best' line. The ML models, trained on the other seven contexts prior to estimation, are: random forest (RF) and gradient boosting (GB). The measurement-time axis is logarithmic, and the first and second vertical dotted lines mark the times at which $1000$ and $10000$ detections are accumulated, respectively, per dataset.
• Figure 4: Density plots of estimate comparisons between OLS models and least-squares fitting. Each red density 'cloud' represents $500$ context-specific histograms containing a certain number of coincidences, e.g. $1000$ detections for the 1p2uW context. For each histogram, the least-squares fit suggests a $g$ value along the $x$ axis and the transferred OLS model suggests a $g$ value along the $y$ axis. The dashed diagonal indicates where both estimates would be the same, and the black circle denotes the ground truth. The 'x' marks the average prediction of both approaches. Per plot, axis scales are equal. For considerations of space, only five contexts are shown. Note that if the OLS model is tested on $500$ size-$1000000$ histograms, it was trained on $2000\times7$ size-$1000000$ histograms from seven other contexts.
• Figure 5: Density plots of estimate comparisons between RF models and least-squares fitting. Each red density 'cloud' represents $500$ context-specific histograms containing a certain number of coincidences, e.g. $1000$ detections for the 1p2uW context. For each histogram, the least-squares fit suggests a $g$ value along the $x$ axis and the transferred RF model suggests a $g$ value along the $y$ axis. The dashed diagonal indicates where both estimates would be the same, and the black circle denotes the ground truth. The 'x' marks the average prediction of both approaches. Per plot, axis scales are equal. For considerations of space, only five contexts are shown. Note that if the RF model is tested on $500$ size-$1000000$ histograms, it was trained on $400\times7$ size-$1000000$ histograms from seven other contexts.