Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory but offer higher accuracy. This paper shows that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. While sampling observables reduces the speedup, it's shown that estimating all elements of the *k*-particle reduced density matrix requires only poly-logarithmically scaling samples in basis set size. A more efficient quantum algorithm for first-quantized mean-field state preparation is also introduced. Quantum speedup is most pronounced for finite-temperature simulations, suggesting potential quantum advantage for several practically important electron dynamics problems.

Ryan Babbush, William J. Huggins, Dominic W. Berry, Shu Fay Ung, Andrew Zhao, David R. Reichman, Hartmut Neven, Andrew D. Baczewski, Joonho Lee