Learning Quantum System Disturbance Models with Probabilistic Bayesian Neural Networks

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.