Universal Dynamics with Globally Controlled Analog Quantum Simulators

TL;DR

This paper establishes the conditions under which globally controlled analog quantum simulators can perform universal quantum computation, extends the framework to various physical systems, and demonstrates experimental control techniques for complex quantum dynamics.

Contribution

It provides a necessary and sufficient condition for universality with global control, extends the theory to fermionic and bosonic systems, and introduces direct quantum optimal control for experimental realization.

Findings

Broad class of simulators is universal under global control

Random global pulses induce information scrambling similar to random circuits

Experimental demonstration of engineered multi-body interactions and topological dynamics

Abstract

Analog quantum simulators with global control fields have emerged as powerful platforms for exploring complex quantum phenomena. Despite these advances, a fundamental theoretical question remains unresolved: to what extent can such systems realize universal quantum dynamics under global control? Here we establish a necessary and sufficient condition for universal quantum computation using only global pulse control, proving that a broad class of analog quantum simulators is, in fact, universal. We further extend this framework to fermionic and bosonic systems, including modern platforms such as ultracold atoms in optical superlattices. Moreover, we observe that analog simulators driven by random global pulses exhibit information scrambling comparable to random unitary circuits. In a dual-species neutral-atom array setup, the measurement outcomes anti-concentrate on a $\log N$ timescale despite the presence of only temporal randomness, opening opportunities for efficient randomness generation. To bridge theoretical possibility with experimental reality, we introduce \emph{direct quantum optimal control}, a control framework that enables the synthesis of complex effective Hamiltonians while incorporating realistic hardware constraints. Using this approach, we experimentally engineer three-body interactions outside the blockade regime and demonstrate topological dynamics on a Rydberg-atom array. Experimental measurements reveal dynamical signatures of symmetry-protected-topological edge modes, confirming both the expressivity and feasibility of our method. Our work opens a new avenue for quantum simulation beyond native hardware Hamiltonians, enabling the engineering of effective multi-body interactions and advancing the frontier of quantum information processing with globally-controlled analog platforms.