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Physical review. B./Physical review. B

Adversarial autoencoder ensemble for fast and probabilistic reconstructions of few-shot photon correlation functions for solid-state quantum emitters

Andrew H. Proppe, Kin Long Kelvin Lee, Cristian L. Cortes, Mari Saif, David B. Berkinsky, Tara Šverko, Weiwei Sun, James Cassidy, Mikhail A. Zamkov, Taehyung Kim, Eunjoo Jang, Stephen K. Gray, Brett A. McGuire, Moungi G. Bawendi

Published Jul 29, 2022• 14 citations
Publisher

Abstract

Second-order photon correlation measurements [${g}^{(2)}(\ensuremath{\tau})$ functions] are widely used to classify single-photon emission purity in quantum emitters or to measure the multiexciton quantum yield of emitters that can simultaneously host multiple excitations -- such as quantum dots -- by evaluating the value of ${g}^{(2)}(\ensuremath{\tau}=0)$. Accumulating enough photons to accurately calculate this value is time consuming and could be accelerated by fitting of few-shot photon correlations. Here, we develop an uncertainty-aware, deep adversarial autoencoder ensemble (AAE) that reconstructs noise-free ${g}^{(2)}(\ensuremath{\tau})$ functions from noise-dominated, few-shot inputs. The model is trained with simulated ${g}^{(2)}(\ensuremath{\tau})$ functions that are facilely generated by Poisson sampling time bins. The AAE reconstructions are performed orders-of-magnitude faster, with reconstruction errors and estimates of ${g}^{(2)}(\ensuremath{\tau}=0)$ that are lower in variance and similar in accuracy compared to Maximum likelihood estimation and Levenberg-Marquardt least-squares fitting approaches, for simulated and experimentally measured few-shot ${g}^{(2)}(\ensuremath{\tau})$ functions (\ensuremath{\sim}100 two-photon events) of InP/ZnS/ZnSe and CdS/CdSe/CdS quantum dots. The deep-ensemble model comprises eight individual autoencoders, allowing for probabilistic reconstructions of noise-free ${g}^{(2)}(\ensuremath{\tau})$ functions, and we show that the predicted variance scales inversely with number of shots, with comparable uncertainties to computationally intensive Markov chain Monte Carlo sampling. This work demonstrates the advantage of machine learning models to perform uncertainty-aware, fast, and accurate reconstructions of simple Poisson-distributed photon correlation functions, allowing for on-the-fly reconstructions and accelerated materials characterization of solid-state quantum emitters.

DOI
10.1103/physrevb.106.045425

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Second-order photon correlation measurements [g(2)(\ensuremathτ){g}^{(2)}(\ensuremath{\tau})g(2)(\ensuremathτ) functions] are widely used to classify single-photon emission purity in quantum emitters or to measure the multiexciton quantum yield of emitters that can simultaneously host multiple excitations -- such as quantum dots -- by evaluating the value of g(2)(\ensuremathτ=0){g}^{(2)}(\ensuremath{\tau}=0)g(2)(\ensuremathτ=0). Accumulating enough photons to accurately calculate this value is time consuming and could be accelerated by fitting of few-shot photon correlations. Here, we develop an uncertainty-aware, deep adversarial autoencoder ensemble (AAE) that reconstructs noise-free g(2)(\ensuremathτ){g}^{(2)}(\ensuremath{\tau})g(2)(\ensuremathτ) functions from noise-dominated, few-shot inputs. The model is trained with simulated g(2)(\ensuremathτ){g}^{(2)}(\ensuremath{\tau})g(2)(\ensuremathτ) functions that are facilely generated by Poisson sampling time bins. The AAE reconstructions are performed orders-of-magnitude faster, with reconstruction errors and estimates of g(2)(\ensuremathτ=0){g}^{(2)}(\ensuremath{\tau}=0)g(2)(\ensuremathτ=0) that are lower in variance and similar in accuracy compared to Maximum likelihood estimation and Levenberg-Marquardt least-squares fitting approaches, for simulated and experimentally measured few-shot g(2)(\ensuremathτ){g}^{(2)}(\ensuremath{\tau})g(2)(\ensuremathτ) functions (\ensuremath{\sim}100 two-photon events) of InP/ZnS/ZnSe and CdS/CdSe/CdS quantum dots. The deep-ensemble model comprises eight individual autoencoders, allowing for probabilistic reconstructions of noise-free g(2)(\ensuremathτ){g}^{(2)}(\ensuremath{\tau})g(2)(\ensuremathτ) functions, and we show that the predicted variance scales inversely with number of shots, with comparable uncertainties to computationally intensive Markov chain Monte Carlo sampling. This work demonstrates the advantage of machine learning models to perform uncertainty-aware, fast, and accurate reconstructions of simple Poisson-distributed photon correlation functions, allowing for on-the-fly reconstructions and accelerated materials characterization of solid-state quantum emitters.
Solid-state single-photon emitters (SPEs) are quantum light sources that combine atomlike optical properties with solid-state integration and fabrication capabilities. SPEs are hindered by spectral diffusion, where the emitter's surrounding environment induces random energy fluctuations. Timescales of spectral diffusion span nanoseconds to minutes and require probing single emitters to remove ensemble averaging. Photon correlation Fourier spectroscopy (PCFS) can be used to measure time-resolved single emitter line shapes, but is hindered by poor signal-to-noise ratio in the measured correlation functions at early times due to low photon counts. Here, we develop a framework to simulate PCFS correlation functions directly from diffusing spectra that match well with experimental data for single colloidal quantum dots. We use these simulated datasets to train a deep ensemble autoencoder machine learning model that outputs accurate, noiseless, and probabilistic reconstructions of the noisy correlations. Using this model, we obtain reconstructed time-resolved single dot emission line shapes at timescales as low as 10 ns, which are otherwise completely obscured by noise. This enables PCFS to extract optical coherence times on the same timescales as Hong-Ou-Mandel two-photon interference, but with the advantage of providing spectral information in addition to estimates of photon indistinguishability. Our machine learning approach is broadly applicable to different photon correlation spectroscopy techniques and SPE systems, offering an enhanced tool for probing single emitter line shapes on previously inaccessible timescales.
Identifying single photon emitters from large, inhomogeneous candidate populations is key to realizing many quantum applications. This requires measuring the emitters second order autocorrelation function, whose statistical reliability is fundamentally limited by acquisition time. Machine learning classifiers can accelerate identification from sparse data, but their performance relative to physics-based inference has not been systematically examined. Here, we introduce sequential Bayesian inference for single photon emitter classification and benchmark it against Levenberg-Marquardt fitting and a feedforward neural network. We use synthetic training and test data calibrated against real Hanbury Brown-Twiss measurements from hexagonal boron nitride emitters, enabling evaluation against an exactly known ground-truth emitter number under realistic noise and background conditions. All three approaches achieve high, near-perfect accuracy with sufficient integration time, but differ greatly in convergence rate and robustness under sparse photon statistics. The neural network is most robust at short integration times. The Bayesian classifier reaches near-perfect accuracy fastest, while retaining full physical interpretability. Levenberg-Marquardt fitting remains a valuable, fully interpretable method, achieving the highest recall despite being the slowest to converge. These results lead to several key conclusions. No single method dominates across all performance metrics. Relying on any one metric alone can give a misleading picture of classifier performance, particularly under sparse photon statistics. Physics-based and data-driven methods are complementary rather than competing approaches. Together, these findings provide practical guidance for selecting and combining classification strategies for scalable single-photon-source screening and other quantum-emitter characterization tasks.
Deep neural network models can be used to learn complex dynamics from data and reconstruct sparse or noisy signals, thereby accelerating and augmenting experimental measurements. Evaluating the quantum optical properties of solid-state single-photon emitters is a time-consuming task that typically requires interferometric photon correlation experiments, such as Photon correlation Fourier spectroscopy (PCFS) which measures time-resolved single emitter lineshapes. Here, we demonstrate a latent neural ordinary differential equation model that can forecast a complete and noise-free PCFS experiment from a small subset of noisy correlation functions. By encoding measured photon correlations into an initial value problem, the NODE can be propagated to an arbitrary number of interferometer delay times. We demonstrate this with 10 noisy photon correlation functions that are used to extrapolate an entire de-noised interferograms of up to 200 stage positions, enabling up to a 20-fold speedup in experimental acquisition time from $\sim$3 hours to 10 minutes. Our work presents a new approach to greatly accelerate the experimental characterization of novel quantum emitter materials using deep learning.
Machine learning models can learn from data samples to carry out various tasks efficiently. When data samples are adversarially manipulated, such as by insertion of carefully crafted noise, it can cause the model to make mistakes. Quantum machine learning models are also vulnerable to such adversarial attacks, especially in image classification using variational quantum classifiers. While there are promising defenses against these adversarial perturbations, such as training with adversarial samples, they face practical limitations. For example, they are not applicable in scenarios where training with adversarial samples is either not possible or can overfit the models on one type of attack. In this paper, we propose an adversarial training-free defense framework that utilizes a quantum autoencoder to purify the adversarial samples through reconstruction. Moreover, our defense framework provides a confidence metric to identify potentially adversarial samples that cannot be purified the quantum autoencoder. Extensive evaluation demonstrates that our defense framework can significantly outperform state-of-the-art in prediction accuracy (up to 68%) under adversarial attacks.
Quantum optics experiments, involving the measurement of low-probability photon events, are known to be extremely time-consuming. We present a methodology for accelerating such experiments using physically motivated ansatzes together with simple statistical learning techniques such as Bayesian maximum a posteriori estimation based on few-shot data. We show that it is possible to reconstruct time-dependent data using a small number of detected photons, allowing for fast estimates in under a minute and providing a one-to-two order of magnitude speed-up in data acquisition time. We test our approach using real experimental data to retrieve the second order intensity correlation function, G(2)(τ), as a function of time delay τ between detector counts, for thermal light as well as anti-bunched light emitted by a quantum dot driven by periodic laser pulses. The proposed methodology has a wide range of applicability and has the potential to impact the scientific discovery process across a multitude of domains.
Evaluating the quantum optical properties of solid-state single-photon emitters is a time-consuming task that typically requires interferometric photon correlation experiments. Photon correlation Fourier spectroscopy (PCFS) is one such technique that measures time-resolved single-emitter line shapes and offers additional spectral information over Hong-Ou-Mandel two-photon interference but requires long experimental acquisition times. Here, we demonstrate a neural ordinary differential equation model, g2NODE, that can forecast a complete and noise-free interferometry experiment from a small subset of noisy correlation functions. We demonstrate this for simulated and experimental data, where g2NODE utilizes 10-20 noisy measured photon correlation functions to create entire denoised interferograms of up to 200 stage positions, enabling up to a 20-fold speedup in experimental acquisition time from hours to minutes. Our work presents a new deep learning approach to greatly accelerate the use of photon correlation spectroscopy as an experimental characterization tool for novel quantum emitter materials.