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Characterizing Non-Markovian Dynamics of Open Quantum Systems

Sohail Reddy

TL;DR

This work addresses the challenge of characterizing non-Markovian dynamics in open quantum systems by applying a structure-preserving, grey-box TCL master equation framework. It compares two parameterizations—Karhunen-Loeve (with Exponential and Squared-Exponential kernels) and neural networks—across linear and nonlinear TCL forms, trained on experimental data from a superconducting qubit in LLNL's QuDIT. Key findings show that KL-based parameterizations yield the most accurate predictions within the training domain, while extrapolation benefits from simpler, affine-like models; nonlinear TCL offers comparable performance for single-qubit dynamics. These insights advance efficient, interpretable modeling for quantum control and error mitigation in near-term quantum devices.

Abstract

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.

Characterizing Non-Markovian Dynamics of Open Quantum Systems

TL;DR

This work addresses the challenge of characterizing non-Markovian dynamics in open quantum systems by applying a structure-preserving, grey-box TCL master equation framework. It compares two parameterizations—Karhunen-Loeve (with Exponential and Squared-Exponential kernels) and neural networks—across linear and nonlinear TCL forms, trained on experimental data from a superconducting qubit in LLNL's QuDIT. Key findings show that KL-based parameterizations yield the most accurate predictions within the training domain, while extrapolation benefits from simpler, affine-like models; nonlinear TCL offers comparable performance for single-qubit dynamics. These insights advance efficient, interpretable modeling for quantum control and error mitigation in near-term quantum devices.

Abstract

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.

Paper Structure

This paper contains 9 sections, 26 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Non-Markovian Master Equation
  3. Characterizing Master Equation
  4. Karhunen-Loeve Expansion Parameterization
  5. Neural Network Parameterization
  6. Characterizing Dynamics of LLNL Testbed's QPUs
  7. Problem Formulation
  8. Characterizing Noisy QPUs
  9. Conclusion

Figures (2)

  • Figure 1: Evolution of the bloch vector components corresponding to the density matrices predicted by the (top) linear TCL and (bottom) nonlinear TCL master equations using various parameterization of the process coefficients.
  • Figure 2: Probability distribution of the trace-distance between the measured density matrices and those predicted by the (top) linear TCL and (bottom) nonlinear TCL master equations. (a,c) represent the trace distance from evolution within the training window and (b,d) represent the trace distance for evolution beyond the training window (i.e. extrapolation).