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

Area of Science:

• Quantum dynamics simulations
• Theoretical chemistry
• Condensed matter physics

Background:

• The generalized quantum master equation (GQME) offers a robust framework for simulating electronic dynamics.
• GQME accounts for nuclear motion and projected-out electronic coherences via memory kernels and inhomogeneous terms.

Purpose of the Study:

• To benchmark quantum simulations of electronic dynamics in a spin-boson model using various GQMEs.
• To assess the accuracy of approximate memory kernels and inhomogeneous terms by comparing them with exact ones derived from TT-TFD.
• To analyze the computational cost scaling of full and reduced-dimensionality GQMEs.

Main Methods:

• Utilized tensor-train thermo-field dynamics (TT-TFD) for exact short-time quantum dynamics simulations.
• Derived exact memory kernels and inhomogeneous terms from TT-TFD simulations.
• Compared exact GQME inputs with those from an approximate linearized semiclassical method.
• Analyzed computational costs for different GQME dimensionalities.

Main Results:

• Benchmark simulations demonstrated the accuracy of TT-TFD derived memory kernels.
• Identified key factors influencing the computational cost scaling of GQMEs.
• Provided insights into inaccuracies arising from approximate input methods in GQME approaches.

Conclusions:

• Exact memory kernels from TT-TFD are crucial for accurate GQME simulations.
• Understanding computational cost scaling is essential for efficient GQME implementation.
• This work facilitates the development of quantum circuits for GQME simulations on digital quantum computers.