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 seminar, I will give a brief introductory course on LCU . I will then demonstrate our LCU implementation on an ion trap quantum computer for calculating squared overlaps |⟨ψ(t=0)|ψ(t>0)⟩|^2 of time-evolved states. Our method is 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⌈log2(L)⌉(2n+1)−n−2. We test this approach by simulating a Rabi-Hubbard Hamiltonian.