REQWIEM: A Grid-Based Wavepacket Propagation Method for Efficient Nonadiabatic Quantum Molecular Dynamics

Nonadiabatic quantum chemistry has several major computational bottlenecks, with tensor network methods failing to efficiently handle long evolution times, highly entangled systems, nonhierarchical correlation, and nonlocalized wavefunctions. Quantum computing has been shown to be a promising avenue both in analog and in digital. Grid based methods have largely been unconsidered, with high overhead of logical qubits requiring fault-tolerance and quantum computers of a scale far beyond what is offered today. REQWIEM is an wavepacket propagation algorithm that leverages a logarithmic-scaling basis of discrete positions to store the wavefunction. VQE efficiently initializes independent wavefunctions on modular registers, where a trotterization provides efficient application of multi-channel coupling and off-diagonal potential terms. We show the application of any smooth potential, piecewise and smooth couplings, and accurate results for conical intersections, photoexcitation, absorption, and chemical scattering. In addition, we exhibit the recovery of scattering amplitudes and cross sections in a quantum computational framework without the precomputation of eigenvalues. This method naturally extends to spin-dependent and strong-field driven systems. REQWIEM compilation requires significantly fewer gates than QSP and Qubitization methods in the same basis and has projected superiority to ML-MCTDH and tDMRG for nonhierarchical systems with more than 6 degrees of freedom.