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arXiv:2401.09822 · AVS Quantum Science

Data-driven characterization of latent dynamics on quantum testbeds

Sohail R. Reddy, Stefanie Günther, Yujin Cho

Published Jul 18, 2024• 0 citations
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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 (QPUs) 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.

DOI
10.1116/5.0204409

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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 (QPUs) 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.
Characterizing non-Markovian quantum dynamics is essential for accurately modeling open quantum systems, particularly in near-term quantum technologies. In this work, we develop a structure-preserving approach to characterizing non-Markovian evolution using the time-convolutionless (TCL) master equation, considering both linear and nonlinear formulations. To parameterize the master equation, we explore two distinct techniques: the Karhunen-Loeve (KL) expansion, which provides an optimal basis representation of the dynamics, and neural networks, which offer a data-driven approach to learning system-environment interactions. We demonstrate our methodology using experimental data from a superconducting qubit at the Quantum Device Integration Testbed (QuDIT) at Lawrence Livermore National Laboratory (LLNL). Our results show that while neural networks can capture complex dependencies, the KL expansion yields the most accurate predictions of the qubit's non-Markovian dynamics, highlighting its effectiveness in structure-preserving quantum system characterization. These findings provide valuable insights into efficient modeling strategies for open quantum systems, with implications for quantum control and error mitigation in near-term quantum processors.
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Inferring the dynamical generator of a many-body quantum system from measurement data is essential for the verification, calibration, and control of quantum processors. When the system is open, this task becomes considerably harder than in the purely unitary case, because coherent and dissipative mechanisms can produce similar measurement statistics and long-time data can be insensitive to coherent couplings. Here we tackle this so-called Lindbladian learning problem of open-system characterisation with maximum-likelihood on Pauli measurements at multiple experimentally friendly \emph{transient} times, exploiting the richer information content of transient dynamics. To navigate the resulting non-convex likelihood loss-landscape, we augment the physical model neural differential-equation term, which is progressively removed during training to distil an interpretable Lindbladian solution. Our method reliably learns open-system dynamics across neutral-atom (with 2D connectivity) and superconducting Hamiltonians, as well as the Heisenberg XYZ, and PXP models on a spin-1/2 chain. For the dissipative part, we show robustness over phase noise, thermal noise, and their combination. Our algorithm can robustly infer these dissipative systems over noise-to-signal ratios spanning four orders of magnitude, and system sizes up to N=6N=6N=6 qubits with fewer than 5×1055 \times 10^55×105 shots.
The core objective of machine-assisted scientific discovery is to learn physical laws from experimental data without prior knowledge of the systems in question. In the area of quantum physics, making progress towards these goals is significantly more challenging due to the curse of dimensionality as well as the counterintuitive nature of quantum mechanics. Here we present the QNODE, a latent neural ordinary differential equation (ODE) trained on expectation values of closed and open-quantum-systems dynamics. It can learn to generate such measurement data and extrapolate outside of its training region that satisfies the von Neumann and time-local Lindblad master equations for closed and open quantum systems, respectively, in an unsupervised means. Furthermore, the QNODE rediscovers quantum-mechanical laws such as the Heisenberg's uncertainty principle in a data-driven way, without any constraint or guidance. Additionally, we show that trajectories that are generated from the QNODE that are close in its latent space have similar quantum dynamics while preserving the physics of the training system.
Motivated by the noisy and fluctuating behavior of current quantum computing devices, this paper presents a data-driven characterization approach for estimating transition frequencies and decay times in a Lindbladian dynamical model of a superconducting quantum device. The data includes parity events in the transition frequency between the first and second excited states. A simple but effective mathematical model, based upon averaging solutions of two Lindbladian models, is demonstrated to accurately capture the experimental observations. A deterministic point estimate of the device parameters is first performed to minimize the misfit between data and Lindbladian simulations. These estimates are used to make an informed choice of prior distributions for the subsequent Bayesian inference. An additive Gaussian noise model is developed for the likelihood function, which includes two hyper-parameters to capture the noise structure of the data. The outcome of the Bayesian inference are posterior probability distributions of the transition frequencies, which for example can be utilized to design risk neutral optimal control pulses. The applicability of our approach is demonstrated on experimental data from the Quantum Device and Integration Testbed (QuDIT) at Lawrence Livermore National Laboratory, using a tantalum-based superconducting transmon device.
Modeling open quantum dynamics without full knowledge of the system Hamiltonian or noise model is a key challenge in quantum control and quantum state estimation. We introduce an Augmented Quantum Neural Ordinary Differential Equation (AQNODE) framework that learns quantum trajectories and dissipation parameters directly from partial continuous measurement data. By embedding the system into a latent space evolved via neural ODEs, AQNODE captures both observable and hidden non-Markovian dynamics with temporal smoothness and physical consistency. Our approach integrates weak measurement data to reconstruct qubit states and time-dependent decoherence rates, enabling accurate state prediction and parameter inference without explicit physical equations. Furthermore, we incorporate AQNODE-based feedback control techniques, including proportional-derivative and time-varying linear-quadratic regulator (LQR) strategies, to steer the quantum system toward target states in real time. Extensive numerical simulations demonstrate AQNODE's ability to generalize across system configurations, achieve low prediction errors, and perform robust quantum filtering and control. These results establish AQNODE as a scalable, differentiable, and experimentally compatible framework for real-time modeling and control of dissipative quantum systems.