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

Understand

We present a product formula to approximate the exponential of a skew-Hermitian operator that is a sum of generators of a Lie algebra.

• The number of terms in the product depends on the structure factors.
• When the generators have large norm with respect to the dimension of the Lie algebra, or when the norm of the effective operator resulting from nested commutators is less than the product of the norms, the number of terms in the product is significantly less than that obtained from well-known results.
• We apply our results to construct product formulas useful for the quantum simulation of some continuous-variable and bosonic physical systems, including systems whose potential is not quadratic.