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arXiv:2502.18426 · The Journal of Chemical Physics

Repeated interaction scheme for the quantum simulation of non-Markovian electron transfer dynamics

Lea Northcote Sørensen, Matthew S. Teynor, Gemma C. Solomon

Published Jun 13, 2025• 3 citations
arXivHTMLPDF

Abstract

Quantum algorithms have the potential to revolutionize our understanding of open quantum systems in chemistry. In this work, we demonstrate that a repeated interaction model, which could serve as the foundation for a digital quantum algorithm, can effectively reproduce non-Markovian electron transfer dynamics under four different donor-acceptor parameter regimes and for a donor-bridge-acceptor system. We systematically explore how the model scales for the regimes. Notably, our approach exhibits favorable scaling in the required repeated interaction duration as the electronic coupling, temperature, damping rate, and system size increase. Furthermore, a single Trotter step per repeated interaction leads to an acceptably small error, and high-fidelity initial states can be prepared with a short time evolution. This efficiency highlights the potential of the model for tackling increasingly complex systems. When fault-tolerant quantum hardware becomes available, algorithms based on this model could be extended to incorporate structured baths, additional energy levels, or more intricate coupling schemes, enabling the simulation of real-world open quantum systems that remain beyond the reach of classical computation.

DOI
10.1063/5.0268071

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Quantum algorithms have the potential to revolutionize our understanding of open quantum systems in chemistry. In this work, we demonstrate that a repeated interaction model, which could serve as the foundation for a digital quantum algorithm, can effectively reproduce non-Markovian electron transfer dynamics under four different donor-acceptor parameter regimes and for a donor-bridge-acceptor system. We systematically explore how the model scales for the regimes. Notably, our approach exhibits favorable scaling in the required repeated interaction duration as the electronic coupling, temperature, damping rate, and system size increase. Furthermore, a single Trotter step per repeated interaction leads to an acceptably small error, and high-fidelity initial states can be prepared with a short time evolution. This efficiency highlights the potential of the model for tackling increasingly complex systems. When fault-tolerant quantum hardware becomes available, algorithms based on this model could be extended to incorporate structured baths, additional energy levels, or more intricate coupling schemes, enabling the simulation of real-world open quantum systems that remain beyond the reach of classical computation.
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While simple spin-boson models have been realized on quantum hardware, simulating extended electronic networks with vibrational environments remains a fundamental challenge in the presence of non-equilibrium, long-lived electronic-vibrational (vibronic) coherence. We present a toolbox for the digital simulation of large open quantum systems with structured environments. It exploits the intrinsic damping of qubits to reproduce vibrational relaxation in combination with a model-specific error mitigation scheme to filter out sources of noise that are not present in the target open system. We simulated a microscopic model of electron-transfer (ET) with a single donor and up to nine acceptor sites on a superconducting processor of IBM, using a model-specific error mitigation scheme. Our results using up to 20 qubits reveal a probability of ET that is well aligned with classical calculations where electronic and vibronic transfer resonances can be identified at the expected driving forces. We conducted 10 independent experiments per system size on different days, accounting for hourly fluctuations in error rates. We find that the most important ingredient for large-scale simulations is a large number of available qubits connected by high-fidelity gates, with coherence times above the threshold set by the target open system. Because the vibronic mechanism of electron transfer is entanglement-driven, our simulation is a natural application-based benchmark, in which the hardware capacity to produce and sustain entanglement is quantified by the maximum system size for which the hardware produces accurate results.
While simple spin-boson models have been realized on quantum hardware, simulating extended electronic networks with local vibrational environments remains a fundamental challenge in the presence of non-equilibrium, long-lived electronic-vibrational (vibronic) coherence. We present a framework for the digital-analog simulation of open quantum systems governed by Hamiltonians with linear-vibronic coupling (LVC) and structured vibrational environments. Our approach exploits the intrinsic dissipation of qubits in near-term quantum hardware as a resource to emulate vibrational relaxation, combined with a model-specific error mitigation scheme to filter out noise sources incompatible with the target open system. We validate our strategy by resolving the vibronic transfer spectra of a one-dimensional donor-acceptor chain on IBM superconducting processors, reproducing non-Markovian dynamics and scaling the chain length up to 10 electronic sites, an unprecedented scale for chemical dynamics on quantum computers. Our model of vibronic electron transfer offers a portable, application-oriented benchmark for simulating long-lived entangled states on NISQ computers.
While simple spin-boson models have been realized on quantum hardware, simulating extended electronic networks with local vibrational environments remains a fundamental challenge in the presence of non-equilibrium, long-lived electronic-vibrational (vibronic) coherence. We present a framework for the digital-analog simulation of open quantum systems governed by Hamiltonians with linear-vibronic coupling (LVC) and structured vibrational environments. Our approach exploits the intrinsic dissipation of qubits in near-term quantum hardware as a resource to emulate vibrational relaxation, combined with a model-specific error mitigation scheme to filter out noise sources incompatible with the target open system. We validate our strategy by resolving the vibronic transfer spectra of a one-dimensional donor-acceptor chain on IBM superconducting processors, reproducing non-Markovian dynamics and scaling the chain length up to 10 electronic sites, an unprecedented scale for chemical dynamics on quantum computers. Our model of vibronic electron transfer offers a portable, application-oriented benchmark for simulating long-lived entangled states on NISQ computers.
A comprehensive description of molecular electron-transfer reactions is essential for our understanding of fundamental phenomena in bioenergetics and molecular electronics.However, experimental studies of molecular systems in condensed-phase environments face difficulties in independently controlling the parameters that govern the transfer mechanism with high precision.We show that, instead, trapped-ion experiments allow us to reproduce and continuously connect vastly different regimes of molecular charge transfer through precise tuning of, e.g., the phonon temperature, electron-phonon interaction, and electronic coupling.Such a setting does not only allow us to reproduce widely used transport models, such as Marcus theory.It also provides access to transfer regimes that are unattainable for molecular experiments, while controlling and measuring the relevant observables on the level of individual quanta.Our numerical simulations predict an unconventional quantum transfer regime, featuring a transition from quantum adiabatic to resonance-assisted transfer as a function of the donor-acceptor energy gap, which can be reached by increasing the electronic coupling at low temperatures.Trapped-ion-based quantum simulations thus promise to enhance our microscopic understanding of molecular electron-transfer processes and may help to reveal efficient design principles for synthetic devices.
We develop randomized quantum algorithms to simulate quantum collision models, also known as repeated interaction schemes, which provide a rich framework to model various open-system dynamics. The underlying technique involves composing time evolutions of the total (system, bath, and interaction) Hamiltonian and intermittent tracing out the environment degrees of freedom. This results in a unified framework where any near-term Hamiltonian simulation algorithm can be incorporated to implement an arbitrary number of such collisions on early fault-tolerant quantum computers: we do not assume access to specialized oracles such as block encodings and minimize the number of ancilla qubits needed. In particular, using the correspondence between Lindbladian evolution and completely positive trace-preserving maps arising out of memoryless collisions, we provide an end-to-end quantum algorithm for simulating Lindbladian dynamics. For a system of nnn-qubits, we exhaustively compare the circuit depth needed to estimate the expectation value of an observable with respect to the reduced state of the system after time ttt while employing different near-term Hamiltonian simulation techniques, requiring at most n+2n+2n+2 qubits in all. We compare the cnot gate counts of the various approaches for estimating the transverse field magnetization of a 10-qubit XX-Heisenberg spin chain under amplitude damping. Finally, we also develop a framework to efficiently simulate an arbitrary number of memory-retaining collisions, i.e., where environments interact, leading to non-Markovian dynamics. Overall, our methods can leverage quantum collision models for both Markovian and non-Markovian dynamics on early fault-tolerant quantum computers, shedding light on the advantages and limitations of simulating open systems dynamics using this framework.