# Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top

## TL;DR

This paper links Trotter errors in digital quantum simulation of collective spins to quantum chaos in the kicked top, showing how chaos onset causes error proliferation and proposing experimental platforms for studying this phenomenon.

## Contribution

It provides a novel interpretation of Trotter errors through quantum chaos theory and demonstrates the feasibility of experimental studies across various quantum platforms.

## Key findings

- Regular kicked top dynamics ensures Trotter error convergence.
- Chaos onset correlates with rapid Trotter error growth.
- Experimental platforms can probe the chaos-error relationship.

## Abstract

This work aims at giving Trotter errors in digital quantum simulation (DQS) of collective spin systems an interpretation in terms of quantum chaos of the kicked top. In particular, for DQS of such systems, regular dynamics of the kicked top ensures convergence of the Trotterized time evolution, while chaos in the top, which sets in above a sharp threshold value of the Trotter step size, corresponds to the proliferation of Trotter errors. We show the possibility to analyze this phenomenology in a wide variety of experimental realizations of the kicked top, ranging from single atomic spins to trapped-ion quantum simulators which implement DQS of all-to-all interacting spin-1/2 systems. These platforms thus enable in-depth studies of Trotter errors and their relation to signatures of quantum chaos, including the growth of out-of-time-ordered correlators.