Multiproduct formulas for time-dependent Hamiltonian simulation

Product formulas, such as Suzuki-Trotter decompositions, are a useful technique for simulating time-dependent (TD) Hamiltonians, such as those with oscillating fields or when working in an interaction picture. In these schemes, the ordering of the operators is chosen to cancel terms in an error series up to a certain order in simulation time $t$. As a generalization of product formulas, multiproduct formulas (MPFs) accomplish this same cancellation of error terms by taking sums of unitaries, which can be implemented on a quantum computer using, for example, the Linear Combination of Unitaries (LCU) technique. While multiproduct formulas have been analyzed in the context of time-independent Hamiltonians, they have not yet been applied to the more general TD case. In this talk, I will present a new algorithm for TD Hamiltonian simulation using MPFs. Like LCU-based methods, our approach has a favorable logarithmic dependence on the inverse error, while also taking advantage of vanishing commutators of $H(t)$ at different times. This work helps address a relative scarcity of algorithms for TD Hamiltonians compared to the time-independent case.