Tensor-Train Thermo-Field Memory Kernels for Generalized Quantum Master Equations

Abstract

The generalized quantum master equation (GQME) approach provides a rigorous framework for deriving the exact equation of motion for any subset of electronic reduced density matrix elements (e.g., the diagonal elements). In the context of electronic dynamics, the memory kernel and inhomogeneous term of the GQME introduce the implicit coupling to nuclear motion or dynamics of electronic density matrix elements that are projected out (e.g., the off-diagonal elements), allowing for efficient quantum dynamics simulations. Here, we focus on benchmark quantum simulations of electronic dynamics in a spin-boson model system described by various types of GQMEs. Exact memory kernels and inhomogeneous terms are obtained from short-time quantum-mechanically exact tensor-train thermo-field dynamics (TT-TFD) simulations. The TT-TFD memory kernels provide insights on the main sources of inaccuracies of GQME approaches when combined with approximate input methods and pave the road for development of quantum circuits that could implement GQMEs on digital quantum computers.

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• Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations
• Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics
• Tensor-Train Split Operator KSL (TT-SOKSL) Method for Quantum Dynamics Simulations
• Functional Tensor-Train Chebyshev Method for Multidimensional Quantum Dynamics Simulations
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• Note: Nonuniqueness of generalized quantum master equations for a single observable

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• Machine learning meets $\mathfrak{su}(n)$ Lie algebra: Enhancing quantum dynamics learning with exact trace conservation
• Toward Quantum-Aware Machine Learning: Improved Prediction of Quantum Dissipative Dynamics via Complex Valued Neural Networks
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• Process Tensor Approaches to Non-Markovian Quantum Dynamics