Southwest Quantum Information and Technology

A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation

Presenting Author: Rolando Somma, (Los Alamos National Laboratory)

We present a product formula to approximate the exponential of a skew-Hermitian operator that is a sum of elements of a Lie algebra. The number of terms in the product depends on the structure factors of the algebra. When the dimension of the algebra is small but the elements have large or unbounded norm, or when the norm of nested commutators is significantly less than the product of the norms, our formula results in a significant improvement upon well-known product formulas in the literature. We apply these results to construct product formulas useful for the quantum simulation of continuous-variable, bosonic physical systems. In these cases, we show that the number of terms in the product can be sublinear or even subpolynomial in the dimension of the relevant local Hilbert spaces, where such a dimension is determined by the energy scale of the problem. Our results emphasize the power of quantum computing for the simulation of various quantum systems.

(Session 7 : Friday from 11:00 am - 11:30 am )