Analog Quantum Simulation of Coupled Electron-Nuclear Dynamics in Molecules

Quantum computing has the potential to reduce the computational cost required for quantum dynamics simulations. However, existing quantum algorithms for coupled electron-nuclear dynamics simulation either require fault-tolerant devices, or involve the Born-Oppenheimer (BO) approximation and pre-calculation of electronic states on classical computers. We present the first quantum simulation approach for molecular vibronic dynamics in a pre-BO framework with an analog mapping of nuclear degrees of freedom, i.e. without the separation of electrons and nuclei, by mapping the molecular Hamiltonian to a device with coupled qubits and bosonic modes. We perform a proof-of-principle emulation of our ansatz using a single-mode model system which represents vibronic dynamics of chemical systems, such as nonadiabatic charge transfer involving polarization of the medium, and propose an implementation of our approach on a trapped-ion device. We show that our approach has exponential savings in resource and computational costs compared to the equivalent classical algorithms. Furthermore, our approach has a much smaller resource and implementation scaling than the existing pre-BO quantum algorithms for chemical dynamics. The low cost of our approach will enable an exact treatment of electron-nuclear dynamics on near-term quantum devices.

💡 Research Summary

This paper introduces the first analog quantum simulation method for molecular vibronic dynamics within a pre‑Born‑Oppenheimer (pre‑BO) framework, eliminating the need to separate electronic and nuclear degrees of freedom. The authors start from the full molecular Hamiltonian expressed in second‑quantized form, where electronic operators are defined over position‑dependent spin orbitals and nuclear vibrational coordinates are represented by mass‑weighted normal modes. By expanding the nuclear‑dependent integrals in a Taylor series around a reference geometry, the Hamiltonian is written as a sum of purely electronic terms, purely nuclear harmonic terms, and mixed electron‑nuclear coupling terms that involve products of fermionic creation/annihilation operators and bosonic ladder operators.

To map this Hamiltonian onto a quantum device, the electronic Fock space is encoded onto Nq qubits using a Jordan‑Wigner transformation, while each vibrational mode is mapped directly onto a bosonic mode of the hardware. The resulting “coupled multi‑qubit‑boson” (cMQB) architecture can be realized on platforms that naturally host both qubits and bosonic modes, such as trapped‑ion systems or circuit‑QED devices. In a trapped‑ion implementation, internal electronic states of the ions represent the qubits (electron occupations) and the collective motional modes of the ion chain serve as the vibrational bosons. The full Hamiltonian becomes a sum of tensor products of Pauli strings and bosonic operators, each of which can be generated with experimentally demonstrated laser‑driven sideband interactions.

The authors demonstrate the approach on a single‑mode vibronic model that captures non‑adiabatic charge‑transfer coupled to medium polarization. Using realistic trapped‑ion parameters (scaling factor F≈10³–10⁴, mode frequencies 1–5 MHz, decoherence times ~0.5 ms), they emulate the dynamics and show excellent agreement with exact classical propagation. Importantly, the analog‑digital hybrid scheme avoids deep Trotter circuits: the electron‑nuclear coupling terms are implemented as native boson‑qubit interactions, dramatically reducing gate depth compared with purely digital algorithms.

A detailed resource analysis reveals exponential savings over classical pre‑BO methods and polynomial scaling relative to existing BO‑based quantum algorithms. While BO‑based variational dynamics require pre‑computed potential‑energy surfaces and non‑adiabatic couplings, the presented method works directly with the full Hamiltonian, eliminating costly classical preprocessing. The qubit count scales linearly with the number of spin orbitals, and the number of bosonic modes scales with the number of vibrational degrees of freedom, leading to a total resource requirement that grows only polynomially with system size. Active‑space techniques further reduce the number of terms by folding inactive orbitals into an effective potential.

The paper discusses extensions to multi‑mode, multi‑electron systems, the possibility of using quasi‑diabatic orbitals to keep the Taylor expansion low‑order, and strategies for error mitigation in near‑term devices. Overall, this work provides a concrete pathway for near‑term quantum hardware to simulate coupled electron‑nuclear dynamics exactly, opening the door to studying phenomena such as intersystem crossing, ultrafast photochemistry, and charge‑transfer processes without relying on the Born‑Oppenheimer approximation.