While the Graybox characterization method allows for implicit noise models and is platform-agnostic, the method lacks uncertainty quantification. Characterization of quantum devices is a crucial process that enables researchers to gain insight from experimental settings. Graybox characterization combines known system dynamics with unknown transformations, where the latter is modeled using machine learning. Prediction uncertainty helps researchers make informed decisions. It allows valuable insights from the devices without overconfidence. We therefore develop a probabilistic Graybox characterization model using probabilistic machine learning, specifically Bayesian Neural Networks, and utilize binary measurement outcomes directly for inference. With stochastic noise in a quantum device, we analyze statistical properties of the measurement data. Our results show that the model's prediction performance solely depends on its ability to capture the expected value of the true expectation value. Our proposed probabilistic Graybox model outperforms the original model by up to 1.9 times in capturing the distribution of observed data. We expect that our results will serve as an additional tool for characterizing quantum devices with uncertainty estimation, as they provide a flexible choice that can be utilized even without extensive prior knowledge of the noise model of the devices.
While the Graybox characterization method allows for implicit noise models and is platform-agnostic, the method lacks uncertainty quantification. Characterization of quantum devices is a crucial process that enables researchers to gain insight from experimental settings. Graybox characterization combines known system dynamics with unknown transformations, where the latter is modeled using machine learning. Prediction uncertainty helps researchers make informed decisions. It allows valuable insights from the devices without overconfidence. We therefore develop a probabilistic Graybox characterization model using probabilistic machine learning, specifically Bayesian Neural Networks, and utilize binary measurement outcomes directly for inference. With stochastic noise in a quantum device, we analyze statistical properties of the measurement data. Our results show that the model's prediction performance solely depends on its ability to capture the expected value of the true expectation value. Our proposed probabilistic Graybox model outperforms the original model by up to 1.9 times in capturing the distribution of observed data. We expect that our results will serve as an additional tool for characterizing quantum devices with uncertainty estimation, as they provide a flexible choice that can be utilized even without extensive prior knowledge of the noise model of the devices.
Quantum sensors offer significant advantages over classical devices in spatial resolution and sensitivity, enabling transformative applications across materials science, healthcare, and beyond. Their practical performance, however, is often constrained by unmodelled effects, including noise, imperfect state preparation, and non-ideal control fields. In this work, we report the first experimental implementation of a graybox modelling strategy for a solid-state open quantum system. The graybox framework integrates a physics-based system model with a data-driven description of experimental imperfections, achieving higher fidelity than purely analytical (whitebox) approaches while requiring fewer training resources than fully deep-learning blackbox models. We experimentally validate the method on the task of estimating a static magnetic field using a single-spin quantum sensor, performing Bayesian inference with a graybox model trained on prior experimental data. Using roughly 10,000 training datapoints, the graybox model yields several orders of magnitude improvement in mean squared error over the corresponding physics-only model, as well as significant improvement over a blackbox model with comparable size. These results are broadly applicable to a wide range of quantum sensing platforms, not limited to single-spin systems, and are particularly valuable for real-time adaptive protocols, where model inaccuracies can otherwise lead to suboptimal control and degraded performance.
Abstract Characterization and calibration of quantum devices are necessary steps to achieve fault-tolerant quantum computing. As quantum devices become more sophisticated, it is increasingly essential to rely not only on physics-based models but also on machine learning models with open-loop optimization. The Graybox approach is a recently proposed platform-agnostic method offering flexibility in modeling the implicit noise. Despite promising results in photonic qubits, its suitability for other platforms is still unknown. We investigate its performance and limitations under realistic conditions, both numerically and experimentally, for the characterization and calibration of gates on superconducting-qubit devices. We find that the Graybox approach performs well on the devices’ pulse-level controls and is able to search for pulse shapes of high-fidelity gates. However, an important limiting factor of the model’s ability to reduce the training errors is the finite number of measurement shots. We therefore derive analytical bounds to explain this limitation, and use them to indicate users whether the characterization performance is optimized. Furthermore, the model’s predictability also depends on other factors such as parameter drift that may occur between the characterization and calibration processes. Our results provide insights into quantum device characterization and gate optimization on superconducting qubits under realistic scenarios using the Graybox approach.
This paper presents a probabilistic machine learning approach that is well suited to learning unknown disturbance dynamics (which may be caused by errors, noise, and parameter variations) in quantum processes or systems from operational data using a Bayesian neural network. This approach considers the dependence of the quantum circuit fidelity (or quantum state output deviation) on the variations of parameters (or factors) such as relaxation time TI, coherence time T2, crosstalk intensity, extra decay, etc. These disturbance factors are used as input variables in the disturbance model, and the quantum circuit fidelity is the output. The respective probability distribution of the weights capturing the disturbance-to-output relationships are learnable parameters of the disturbance model and can be learned from operational data. The learning process may apply to quantify the uncertainty of disturbance in the partial system dynamics, while portions of the nominal system dynamics may be given (or learned from a separate dynamic model). The learned stochastic quantum disturbance models together with the known nominal physical models can be used in the design of quantum system optimal control. As an example, two cases about the applications of probabilistic modeling are studied to learn the noise dynamics in a particular quantum circuit based on simulated datasets. The results are analyzed in different scenarios, and a plan for future work is identified.
The astounding acceleration in Artificial Intelligence and Quantum Computing advances naturally gives rise to a line of research, which unrolls the potential advantages of quantum computing on classical Machine Learning tasks, known as Quantum Machine Learning or Quantum Machine Intelligence. The typical objectives are either (1) exploring the potential quantum advantages on classical learning tasks or (2) levering well-established classical ML algorithms to tackle quantum-related problems on Noisy Intermediate-Scale Quantum (NISQ) devices. Along the second research direction, we study Quantum Neural Networks (QNNs) to accomplish the purpose of Bayesian learning. By observing a wide range of studies on QNNs, in which the sole training method is based on frequentist training, we find that Bayesian learning benefits QNNs from two aspects. First, Bayesian-trained models enjoy a high level of generalization due to the prior and posterior distribution usage compared to frequentist training, which will be justified by this paper’s theoretical study of model capacity. Second, Bayesian Inference offers epistemic uncertainty estimation, which merits the decision-making process. It is worth mentioning that frequentist-trained QNNs generally lack this desirable property. Under the Bayesian training procedure, our derived models can be considered a new class of QNNs (called BayesianQNNs) which possesses both desirable properties of Bayesian Inference while maintaining comparable predictive performance as frequentist counterparts. The proposed Bayesian Quantum Neural Networks is justified by empirical evidence from numerical experiments.
Abstract We show that ensembles of deep neural networks, called deep ensembles, can be used to perform quantum parameter estimation while also providing a means for quantifying uncertainty in parameter estimates, which is a key advantage of using Bayesian inference for parameter estimation that is lost when using existing machine learning methods. We show that optimizing for both accurate parameter estimates and well calibrated uncertainty estimates does not lead to degradation in the former as opposed to only optimizing for accuracy. We also show that the drift detection capabilities of these ensemble models can be used to detect drift in the experimental data used during inference. This approach is also shown to provide much faster inference time than both likelihood-based and likelihood-free Bayesian inference. These results suggest that such models could enable accurate, real-time parameter estimation with quantified uncertainty, making them promising candidates for deployment in experimental settings.
Abstract Bayesian estimation is a powerful theoretical paradigm for the operation of the approach to parameter estimation. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its use to systems that can be explicitly modeled. In this theoretical study, we formulate parameter estimation as a classification task and use artificial neural networks to efficiently perform Bayesian estimation. We show that the network’s posterior distribution is centered at the true (unknown) value of the parameter within an uncertainty given by the inverse Fisher information, representing the ultimate sensitivity limit for the given apparatus. When only a limited number of calibration measurements are available, our machine-learning-based procedure outperforms standard calibration methods. Our machine-learning-based procedure is model independent, and is thus well suited to “black-box sensors”, which lack simple explicit fitting models. Thus, our work paves the way for Bayesian quantum sensors that can take advantage of complex nonclassical quantum states and/or adaptive protocols. These capabilities can significantly enhance the sensitivity of future devices.