Work

Harnessing subspace controllability: Dynamical generation of Dicke states in Heisenberg-coupled qubit arrays with a single local control

Year: 2026

Type: article

Abstract: We explore the feasibility of realizing Dicke states in qubit arrays with always-on isotropic Heisenberg coupling between adjacent qubits, assuming a single Zeeman-type control acting in the z direction on an actuator qubit. The Lie-algebraic criteria of controllability imply that such an array is not completely controllable, but satisfies the conditions for subspace controllability on any subspace with a fixed number of excitations. Therefore, a qubit array described by the model under consideration is state-to-state controllable for an arbitrary choice of initial and final states that have the same Hamming weight. This limited controllability is exploited here for the time-efficient dynamical generation of an a -excitation Dicke state | D a N 〉 ( a = 1 , 2 , ... , N − 1 ) in a linear array with N qubits starting from a generic Hamming-weight- a product state. To dynamically generate the desired Dicke states—including W states | W N 〉 as their special ( a = 1 ) case—in the shortest possible time with a single local Z control, we employ an optimal-control scheme based on the (dCRAB) algorithm. We optimize the target-state fidelity over the expansion coefficients of smoothly varying control fields in a truncated random Fourier basis; this is done by combining Nelder-Mead-type local optimizations with the multistart-based clustering algorithm that facilitates searches for global extrema. In this manner, we obtain the optimal-control fields for Dicke-state preparation in arrays with up to nine qubits. Based on our numerical results, we find that the shortest possible state-preparation times scale as O ( N 2.08 ) for W states and O ( N 1.78 ) for a = 2 Dicke states. Finally, we demonstrate the robustness of our dCRAB-based state-engineering scheme against various types of imperfections of relevance for its anticipated experimental implementation.

Source: Physical Review Research

DOI: 10.1103/t2zk-4nxh

Authors: Vladimir M. Stojanović, Tommaso Calarco, Andrea Muratori

Institutions: Technische Universität Darmstadt, Forschungszentrum Jülich, University of Bologna

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625

Funder: Agence Nationale de la Recherche