Quantum algorithm for simulating non-adiabatic dynamics at metallic surfaces

TL;DR

The paper presents a quantum algorithm to simulate non-adiabatic dynamics at molecule–metal interfaces by generalizing the Anderson–Newns Hamiltonian to include multiple molecular orbitals, nuclear degrees of freedom, and electron correlations. It develops a highly optimized Trotter-based approach that partitions the GAN Hamiltonian into commuting fragments, diagonalizes each fragment with Clifford operations, and exponentiates efficiently using phase-gradient and coefficient-accumulation techniques, aided by caching and QROM-based function evaluations. Resource estimates for realistic models (e.g., 100 metal orbitals, 8 molecular orbitals, 20 nuclear DOFs) indicate the algorithm requires about 271 qubits and around $7.9 \times 10^7$ Toffoli gates for 1000 Trotter steps, suggesting feasibility on first-generation fault-tolerant quantum computers and highlighting non-adiabatic interfacial dynamics as a promising near-term quantum-advantage domain. The work also outlines concrete applications—molecular scattering/adsorption, photoinduced charge transfer, and molecular junction transport—and discusses extensions, including coupling to phonons and improved parameterization from electronic-structure data.

Abstract

Non-adiabatic dynamics at molecule-metal interfaces govern diverse and technologically important phenomena, from heterogeneous catalysis to dye-sensitized solar energy conversion and charge transport across molecular junctions. Realistic modeling of such dynamics necessitates taking into account various charge and energy transfer channels involving the coupling of nuclear motion with a very large number of electronic states, leading to prohibitive cost using classical computational methods. In this work we introduce a generalization of the Anderson-Newns Hamiltonian and develop a highly optimized quantum algorithm for simulating the non-adiabatic dynamics of realistic molecule-metal interfaces. Using the PennyLane software platform, we perform resource estimations of our algorithm, showing its remarkably low implementation cost for model systems representative of various scientifically and industrially relevant molecule-metal systems. Specifically, we find that time evolution for models including $100$ metal orbitals, $8$ molecular orbitals, and $20$ nuclear degrees of freedom, requires only $271$ qubits and $7.9 \times 10^7$ Toffoli gates for $1000$ Trotter steps, suggesting non-adiabatic molecule-metal dynamics as a fruitful application of first-generation fault-tolerant quantum computers.

Figures (1)

• Figure 1: Graphical depiction of various simulation problems that can be tackled by our new algorithm and examples of relevant observables. In the top panels, representative systems involving the non-adiabatic dynamics of molecules interacting with interfaces are depicted: a) coupled ion-electron transfer at a battery electrode in the presence of solvent, b) photo-induced charge transfer from a chromophore to a semiconductor nanoparticle in a dye-sensitized solar cell, and c) current-induced bond rupture in a molecular junction under voltage bias. The bottom panel d) shows examples of time-resolved nuclear and electronic observables of interest extracted via quantum simulation.