Data-Driven Characterization of Latent Dynamics on Quantum Testbeds

TL;DR

This paper augments the dynamical equation of quantum systems described by the Lindblad master equation with a parameterized source term that is trained from experimental data to capture unknown system dynamics, such as environmental interactions and system noise.

Abstract

This paper presents a data-driven approach to learn latent dynamics in superconducting quantum computing hardware. To this end, we augment the dynamical equation of quantum systems described by the Lindblad master equation with a parameterized source term that is trained from experimental data to capture unknown system dynamics, such as environmental interactions and system noise. We consider a structure preserving augmentation that learns and distinguishes unitary from dissipative latent dynamics parameterized by a basis of linear operators, as well as an augmentation given by a nonlinear feed-forward neural network. Numerical results are presented using data from two different quantum processing units (QPU) at Lawrence Livermore National Laboratory's Quantum Device and Integration Testbed. We demonstrate that our interpretable, structure preserving, and nonlinear models are able to improve the prediction accuracy of the Lindblad master equation and accurately model the latent dynamics of the QPUs.

Figures (6)

• Figure 1: Time evolution of the expected energy of a sample experiment (top) and expected trace distance (bottom) on Dev1 (left) and Dev2 (right) compared to the underlying base models. Black line represents experimentally measured data.
• Figure 2: Probability distribution of the trace-distance using UDE models trained with data from all experiments on Dev1 over $10 \upmu$s (left) and $20 \upmu$s (right). Dashed lines represent the training data set while solid lines denote the validation data set.
• Figure 3: Probability distribution of the trace-distance using UDE models trained over a data from a single sample on Dev1 over a $20 \upmu$s window. Dashed and solid lines represent Experiment-Generalized and Experiment-Specific operators, respectively.
• Figure 4: Probability distribution of the trace-distance using UDE models trained over a data from all experiments on Dev2 (Dashed and solid lines represent the measure over training and validation set, respectively).
• Figure 5: Time evolution of expected energy and probability distribution of the trace-distance using UDE models trained over data from a single sample on Dev2 . (For the expected energy, the shaded region represent the data from the experimentally obtained density matrices; for the probability densities, dashed and solid lines represent Experiment-Generalized and Experiment-Specific operators, respectively).