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arXiv:2005.05802 · Physical Review Letters

Bayesian Optimal Control of Greenberger-Horne-Zeilinger States in Rydberg Lattices

Rick Mukherjee, Harry Xie, Florian Mintert

Published Nov 12, 2020• 34 citations
arXivHTMLPDF

Abstract

The ability to prepare nonclassical states in a robust manner is essential for quantum sensors beyond the standard quantum limit. We demonstrate that Bayesian optimal control is capable of finding control pulses that drive trapped Rydberg atoms into highly entangled Greenberger-Horne-Zeilinger states. The control sequences have a physically intuitive functionality based on the quasi-integrability of the Ising dynamics. They can be constructed in laboratory experiments, resulting in preparation times that scale very favorably with the system size.

DOI
10.1103/physrevlett.125.203603

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The ability to prepare nonclassical states in a robust manner is essential for quantum sensors beyond the standard quantum limit. We demonstrate that Bayesian optimal control is capable of finding control pulses that drive trapped Rydberg atoms into highly entangled Greenberger-Horne-Zeilinger states. The control sequences have a physically intuitive functionality based on the quasi-integrability of the Ising dynamics. They can be constructed in laboratory experiments, resulting in preparation times that scale very favorably with the system size.
The multipartite Greenberger–Horne–Zeilinger (GHZ) states play an important role in large-scale quantum information processing. We utilize the polychromatic driving fields and the engineered spontaneous emissions of Rydberg states to dissipatively drive three- and four-partite neutral atom systems into the steady GHZ states, at the presence of the next-nearest neighbor interaction of excited Rydberg states. Furthermore, the introduction of quantum Lyapunov control can help us optimize the dissipative dynamics of the system so as to shorten the convergence time of the target state, improve the robustness against the spontaneous radiations of the excited Rydberg states, and release the limiting condition for the strengths of the polychromatic driving fields. Under the feasible experimental conditions, the fidelities of three- and four-partite GHZ states can be stabilized at 99.24 % and 98.76 %, respectively.
Entangled many-body states are a key resource for quantum technologies. Yet their preparation through analog control of interacting quantum systems is often hindered by experimental imperfections. Here, we introduce the adiabatic echo protocol, a general approach to state preparation designed to suppress the effect of static perturbations. We provide an analytical understanding of its robustness in terms of dynamically engineered destructive interference. By applying quantum optimal control methods, we demonstrate that such a protocol emerges naturally in a variety of settings, without requiring assumptions on the form of the control fields. Examples include Greenberger-Horne-Zeilinger state preparation in Ising spin chains and two-dimensional Rydberg atom arrays, as well as the generation of quantum spin liquid states in frustrated Rydberg lattices. Our results highlight the broad applicability of this protocol, providing a practical framework for reliable many-body state preparation in present-day quantum platforms.
We propose a scalable protocol in the Rydberg atomic system to generate the Greenberger-Horne-Zeilinger (GHZ) states, where the qubits are encoded on the hyperfine ground levels. Our system is featured with off-resonant driving fields rather than strong Rydberg interaction sufficient for blockade. Closely it can follow the desired nonadiabatic passage during the time evolution and avoid the unwanted transition by imposing the passage-dependent and fast-varying global phase, that serves as an error correction to the universal quantum control. In our protocol, an NNN-qubit GHZ state is prepared in N−1N-1N−1 steps, which is found to be robust against both environmental noise and systematic deviation. Our protocol therefore provides an avenue toward large-scale entanglement, which is essential for quantum information processing and computation based on neutral atoms.
The ability to engineer and control quantum states of many-body systems is a central challenge in quantum information science. For a register of NNN qubits, the full Hilbert space dimension grows exponentially as 2N2^N2N, rendering generic state preparation and control infeasible without exploiting structure or symmetry. A particularly important and physically motivated restriction is to the fully symmetric subspace, spanned by the Dicke states, which are simultaneous eigenstates of collective spin J=N/2J=N/2J=N/2. Ensembles of Rydberg atoms interacting via electric dipoles in two-dimensional tweezer arrays form a promising platform for achieving such control. However, the finite range of dipole-dipole interactions poses a challenge to generating and controlling the Dicke manifold because the Hamiltonian incurs leakage from the computational subspace. To counteract this leakage, we perform quantum optimal control algorithms on a truncated Hilbert space according to our newly developed method of ``irrep distillation'' (IRD), which captures the process by which the symmetric subspace couples to leakage error-spaces, using only linear-scaling Hilbert dimension. We implement gradient ascent pulse engineering (GrAPE) on control schemes with little or no local addressing, to generate resourceful states like Greenberger-Horne-Zeilinger, Dicke, and extremal quantum states. We benchmark each scheme of IRD-GrAPE for its quantum speed limit (QSL), as well as exactly testing pulse fidelities on small system sizes and predicting fidelities using higher-order IRD on larger systems.
Realising high fidelity entangled states in controlled quantum many-body systems is challenging due to experimental uncertainty in a large number of physical quantities. We develop a robust optimal control method for achieving this goal in finite-size multi-qubit systems despite significant uncertainty in multiple parameters. We demonstrate its effectiveness in the generation of the Greenberger-Horne-Zeilinger state on a star graph of capacitively coupled transmons, and discuss its crucial role for achieving the Heisenberg limit of precision in quantum sensing.
We present a quantum optimal control protocol to generate highly spin-squeezed states in Rydberg atom arrays coupled via Ising-type van der Waals interactions. Using gradient-based optimization techniques, we construct time-dependent pulse sequences that steer an initial product state toward highly entangled, spin-squeezed states with predefined magnetization and squeezing axes. We focus on the Wineland parameter ${\ensuremath{\xi}}_{W}^{2}$ to measure spin squeezing, and our approach achieves near-optimal spin squeezing in one-dimensional ring arrays of up to N=8N=8N=8 spins, significantly outperforming conventional quench dynamics for all system sizes studied. Remarkably, optimized pulse sequences can be directly scaled to larger arrays without additional optimization, achieving a squeezing parameter as low as ${\ensuremath{\xi}}_{W}^{2}=0.227$ in systems containing N=50N=50N=50 spins. This work demonstrates the potential of quantum optimal control methods for preparing highly spin-squeezed states, opening pathways to enhanced quantum metrology.