# Robust Dynamic Hamiltonian Engineering of Many-Body Spin Systems

## TL;DR

This paper presents a systematic method for designing robust control pulse sequences to engineer desired Hamiltonians in many-body quantum systems, improving coherence, sensing, and simulation capabilities.

## Contribution

It introduces a matrix-based algebraic framework for creating robust, efficient pulse sequences applicable to complex many-body Hamiltonians, with experimental validation.

## Key findings

- Designed pulse sequences enhance quantum coherence and robustness.
- Framework accelerates numerical search for optimal sequences.
- Experimental demonstration confirms robustness in general interaction systems.

## Abstract

We introduce a new approach for the robust control of quantum dynamics of strongly interacting many-body systems. Our approach involves the design of periodic global control pulse sequences to engineer desired target Hamiltonians that are robust against disorder, unwanted interactions and pulse imperfections. It utilizes a matrix representation of the Hamiltonian engineering protocol based on time-domain transformations of the Pauli spin operator along the quantization axis. This representation allows us to derive a concise set of algebraic conditions on the sequence matrix to engineer robust target Hamiltonians, enabling the simple yet systematic design of pulse sequences. We show that this approach provides an efficient framework to (i) treat any secular many-body Hamiltonian and engineer it into a desired form, (ii) target dominant disorder and interaction characteristics of a given system, (iii) achieve robustness against imperfections, (iv) provide optimal sequence length within given constraints, and (v) substantially accelerate numerical searches of pulse sequences. Using this systematic approach, we develop novel sets of pulse sequences for the protection of quantum coherence, optimal quantum sensing and quantum simulation. Finally, we experimentally demonstrate the robust operation of these sequences in a system with the most general interaction form.