Hamiltonian dynamics simulation using linear combination of unitaries on an ion trap quantum computer (2501.18515v2)

Abstract: The linear combination of unitaries (LCU) method has proven to scale better than existing product formulas in simulating long time Hamiltonian dynamics. However, given the number of multi-control gate operations in the standard prepare-select-unprepare architecture of LCU, it is still resource-intensive to implement on the current quantum computers. In this work, we demonstrate LCU implementations on an ion trap quantum computer for calculating squared overlaps $|\langle \psi(t=0)|\psi(t>0)\rangle|^2$ of time-evolved states. This is achieved by an optimized LCU method, based on pre-selecting relevant unitaries, coupled with a compilation strategy which makes use of quantum multiplexor gates, leading to a significant reduction in the depth and number of two-qubit gates in circuits. For $L$ Pauli strings in a Taylor series expanded $n$-qubit-mapped time evolution operator, we find a two-qubit gate count of $2^{\lceil log_2(L)\rceil}(2n+1)-n-2$. We test this approach by simulating a Rabi-Hubbard Hamiltonian.