Hamiltonian dynamics simulation using linear combination of unitaries on an ion trap quantum computer

TL;DR

This paper demonstrates an optimized implementation of the linear combination of unitaries (LCU) method for simulating Hamiltonian dynamics on an ion trap quantum computer, reducing resource requirements significantly.

Contribution

The authors develop an optimized LCU approach using pre-selection and quantum multiplexor gates, enabling more efficient Hamiltonian simulations on current quantum hardware.

Findings

Achieved reduced two-qubit gate count for LCU implementation.

Successfully simulated a Rabi-Hubbard Hamiltonian.

Provided a scalable method for Hamiltonian dynamics simulation.

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.