Generalized Hamiltonian to describe imperfections in ion-light interaction

TL;DR

This paper derives a comprehensive Hamiltonian model for ion-light interactions in trapped-ion systems, accounting for imperfections and experimental effects, to improve quantum gate fidelity and guide hardware development.

Contribution

It introduces a generalized Hamiltonian that includes both desired interactions and unwanted effects, validated experimentally for axial mode heating.

Findings

The Hamiltonian captures ion-ion entanglement and imperfections.

Experimental confirmation of axial mode heating effects.

Guidance for improving quantum gate fidelity.

Abstract

We derive a general Hamiltonian that governs the interaction between an $N$-ion chain and an externally controlled laser field, where the ion motion is quantized and the laser field is considered beyond the plane-wave approximation. This general form not only explicitly includes terms that are used to drive ion-ion entanglement, but also a series of unwanted terms that can lead to quantum gate infidelity. We demonstrate the power of our expressivity of the general Hamiltonian by singling out the effect of axial mode heating and confirm this experimentally. We discuss pathways forward in furthering the trapped-ion quantum computational quality, guiding hardware design decisions.