Adiabatic Populations for High-Dimensional Quantum Simulations Using Matrix Product State Sampling

Abstract Electronic state populations are central quantities in nonadiabatic dynamics, with different electronic representations conveying different information. The populations of diabatic states, which preserve electronic character, offer chemically intuitive interpretations of dynamical simulations. The populations of adiabatic states, which are simply the energy-ordered eigenstates of the electronic Hamiltonian, track the electronic relaxation of the system. For high-dimensional quantum simulations, adiabatic populations have remained essentially inaccessible due to the high intrinsic rank of the diabatic-to-adiabatic transformation. Here, we present a method that bypasses this problem, using Ferris and Vidal’s Monte Carlo sampling approach to estimate adiabatic populations from matrix product state (MPS) wave functions. The estimator is unbiased with rigorously bounded statistical error, has computational scaling comparable to propagation, and places no additional restriction on the Hamiltonian. We demonstrate converged adiabatic populations for the 24-mode pyrazine and 78-mode BMA radical cation models, whose contrasting dynamics illustrate the necessity of both electronic representations for interpretation. The sampled configurations further enable trajectory-like analyses of wavepacket dynamics and promise to provide rigorous high-dimensional benchmarks for mixed quantum-classical methods.