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Non-Equilibrium Dynamics for Electrochemistry Simulations on Quantum Computers

Gajewski, Marvin, Dany, Jules, Schellhorn, Arta, Somoza, Alejandro, Horstmann, Birger

Published Jul 29, 2025• 0 citations
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Quantum Simulation of Non-Equilibrium Systems using Adaptive Sampling

Jincheng Zhang

Quantum simulation of non-equilibrium systems presents a significant challenge due to the inherent complexity of these systems and the limitations of classical simulation techniques. Traditional methods often struggle to accurately capture the intricate dynamics arising from non-equilibrium conditions. This paper introduces a novel method, Adaptive Sampling, designed to overcome these limitations. We propose an iterative process where the sampling rate is dynamically adjusted based on the system's evolution, enabling the capture of complex dynamics with greater fidelity and reduced computational cost. The core mechanism centers on employing adaptive sampling to refine the simulation, allowing for the exploration of a wider range of possible states and ultimately, a more accurate representation of the system's behavior. This approach promises to significantly advance the field of quantum simulation, offering a robust and adaptable solution to the challenges associated with simulating non-equilibrium systems.

•Aug 29, 2026•0 citations
The recent advancement of quantum computer hardware offers the potential to simulate quantum many-body systems beyond the capability of its classical counterparts. However, most current works focus on simulating the ground-state properties or pure-state quantum dynamics of quantum systems. Finite-temperature physics are much less explored, and existing literature mainly consider equilibrium properties. Here we present a variational quantum simulation protocol based on the thermofield dynamics formalism to simulate the dynamical and non-equilibrium finite-temperature properties of quantum systems with near-term quantum computers. Compared to previous approaches in computing the equilibrium dynamical properties, our approach does not require the computationally expensive initial state sampling. More importantly, our approach is capable of simulating non-equilibrium phenomena which have not been previously explored with quantum computers. Numerical simulations of molecular absorption spectrum and spin quenched dynamics affirm the capability of our method.
We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case.
Quantum simulation of non-equilibrium systems presents a significant challenge due to the inherent complexity of these systems and the limitations of classical simulation techniques. Traditional methods often struggle to accurately capture the intricate dynamics arising from non-equilibrium conditions. This paper introduces a novel method, Adaptive Sampling, designed to overcome these limitations. We propose an iterative process where the sampling rate is dynamically adjusted based on the system's evolution, enabling the capture of complex dynamics with greater fidelity and reduced computational cost. The core mechanism centers on employing adaptive sampling to refine the simulation, allowing for the exploration of a wider range of possible states and ultimately, a more accurate representation of the system's behavior. This approach promises to significantly advance the field of quantum simulation, offering a robust and adaptable solution to the challenges associated with simulating non-equilibrium systems.