W- and Dicke-state engineering using optimal global control in nearest-neighbor coupled ring-shaped qubit arrays

Motivated by a compelling need for time-efficient and robust schemes for quantum-state engineering in systems of neutral atoms in optical tweezers, we consider a ring-shaped array of qubits with nearest-neighbor Ising-type (zz) coupling and transverse (x and y) global control fields. This system to a large extent mimics - outside of the Rydberg-blockade regime - a circular array of neutral atoms interacting through van-der-Waals type interaction. We investigate the preparation of W and Dicke states in this system starting from the default initial state |00ldots 0rangle using two different optimal-control approaches: (i) NMR-like pulse sequence, which consists of instantaneous (delta-shaped) control- and Ising-interaction pulses, and (ii) time-dependent control scheme, which entails shaped control pulses in the presence of always-on Ising interaction between adjacent qubits. By making use of the underlying dihedral symmetry of this system - which allows one to use a symmetry-adapted computational basis with mathcal{O}\(2^N / N\) states in an N-qubit system - and utilizing advanced global-optimization methods, we find optimal sequences of pulses for realizing W and Dicke states within both approaches. In addition, we demonstrate robustness of these sequences against unavoidable control errors. Finally, using typical values of parameters in realistic Rydberg-atom systems, we show that our control schemes enable the preparation of the desired multiqubit states on time scales much shorter than the relevant coherence times of those systems.