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

TL;DR

This work tackles fast and robust preparation of multipartite entangled states in ring-shaped arrays of Ising-coupled qubits with global transverse control, motivated by neutral-atom platforms. It develops two optimal-control strategies—NMR-like delta-pulse sequences and time-dependent shaped pulses—exploiting dihedral symmetry to manage the large Hilbert-space dimension. The authors demonstrate that $W$ states can be produced with times that scale linearly with the number of qubits, while Dicke states require superlinear times, achieving high fidelities and robustness to control errors. With parameters appropriate for gr-type Rydberg-atom systems in optical tweezers, the schemes yield state-preparation times well below coherence times, indicating practical viability for scalable neutral-atom quantum state engineering.

Abstract

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 $|00\ldots 0\rangle$ 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.

Figures (16)

• Figure 1: Pictorial illustration of a ring-shaped qubit array, with nearest-neighbor Ising-type coupling of strength $J$ and transverse global control fields $B_x(t)$ and $B_y(t)$. The qubits in this system are assumed to be $gr$-type neutral-atom qubits.
• Figure 2: State preparation infidelity of $W$ and Dicke states within the NMR-like scheme, each one represented by a bar indicating the best result achieved. Different colors indicate different values of $N$.
• Figure 3: Example of optimal pulse for $\ket{W_{5}}$ obtained within the NMR-like scheme.
• Figure 4: Best infidelity obtained as a function of $M$ within the NMR-like scheme.
• Figure 5: (a) Minimal number of interaction pulses $M$ necessary for the exact preparation of $W$ and Dicke (up to $k=2$) states, and corresponding (b) average preparation times (error bars indicate the standard deviation of the samples contributing to the average), within the NMR scheme.