# Dynamical engineering of interactions in qudit ensembles

## TL;DR

This paper introduces a method for engineering and controlling interactions in ensembles of qudits using global control fields, enabling decoupling of unwanted interactions and the design of specific Hamiltonians for quantum simulation.

## Contribution

It provides necessary and sufficient conditions for interaction decoupling, a universal decoupling sequence, and an algorithm for Hamiltonian engineering in qudit systems.

## Key findings

- A 6-pulse sequence effectively decouples spin-1 dipolar interactions.
- Engineered a spin-1 Ising chain to explore topological phase transitions.
- Established conditions for interaction decoupling and Hamiltonian design.

## Abstract

We propose and analyze a method to engineer effective interactions in an ensemble of d-level systems (qudits) driven by global control fields. In particular, we present (i) a necessary and sufficient condition under which a given interaction can be turned off (decoupled), (ii) the existence of a universal sequence that decouples any (cancellable) interaction, and (iii) an efficient algorithm to engineer a target Hamiltonian from an initial Hamiltonian (if possible). As examples, we provide a 6-pulse sequence that decouples effective spin-1 dipolar interactions and demonstrate that a spin- 1 Ising chain can be engineered to study transitions among three distinct symmetry protected topological phases.