
A. Kruckenhauser, R. van Bijnen, T. Zache, M. Di Liberto, P. Zoller Highdimensional SO(4)symmetric Rydberg manifolds for quantum simulation,
Quantum Sci. Technol. 8 (20221219),
http://dx.doi.org/10.1088/20589565/aca996 doi:10.1088/20589565/aca996 (ID: 720885)
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We develop a toolbox for manipulating arrays of Rydberg atoms prepared in highdimensional hydrogenlike manifolds in the regime of linear Stark and Zeeman effect. We exploit the SO(4) symmetry to characterize the action of static electric and magnetic fields as well as microwave and optical fields on the wellstructured manifolds of states with principal quantum number n. This enables us to construct generalized largespin Heisenberg models for which we develop statepreparation and readout schemes. Due to the available large internal Hilbert space, these models provide a natural framework for the quantum simulation of Quantum Field Theories, which we illustrate for the case of the sineGordon and massive Schwinger models. Moreover, these highdimensional manifolds also offer the opportunity to perform quantum information processing operations for quditbased quantum computing, which we exemplify with an entangling gate and a statetransfer protocol for the states in the neighborhood of the circular Rydberg level.

M. Di Liberto, A. Kruckenhauser, P. Zoller, M. Baranov Topological phonons in arrays of ultracold dipolar particles,
Quantum 6 731 (20220531),
http://dx.doi.org/10.22331/q20220607731 doi:10.22331/q20220607731 (ID: 720680)
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The notion of topology in physical systems is associated with the existence of a nonlocal ordering that is insensitive to a large class of perturbations. This brings robustness to the behaviour of the system and can serve as a ground for developing new faulttolerant applications. We discuss how to design and study a large variety of topologyrelated phenomena for phononlike collective modes in arrays of ultracold polarized dipolar particles. These modes are coherently propagating vibrational excitations, corresponding to oscillations of particles around their equilibrium positions, which exist in the regime where longrange interactions dominate over singleparticle motion. We demonstrate that such systems offer a distinct and versatile tool to investigate topological effects that can be accessed by choosing the underlying crystal structure and by controlling the anisotropy of the interactions. Our results show that arrays of dipolar particles provide a promising unifying platform to investigate topological phenomena with phononic modes.

C. Dlaska, K. Ender, G. B. Mbeng, A. Kruckenhauser, W. Lechner, R. van Bijnen Quantum optimization via fourbody Rydberg gates,
Phys. Rev. Lett. 128 (20220324),
http://dx.doi.org/10.1103/PhysRevLett.128.120503 doi:10.1103/PhysRevLett.128.120503 (ID: 720749)
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There is a large ongoing research effort towards obtaining a quantum advantage in the solution of combinatorial optimization problems on nearterm quantum devices. A particularly promising platform for testing and developing quantum optimization algorithms are arrays of trapped neutral atoms, lasercoupled to highly excited Rydberg states. However, encoding combinatorial optimization problems in atomic arrays is challenging due to the limited interqubit connectivity given by their native finiterange interactions. Here we propose and analyze a fast, high fidelity fourbody Rydberg parity gate, enabling a direct and straightforward implementation of the LechnerHaukeZoller (LHZ) scheme and its recent generalization, the parity architecture, a scalable architecture for encoding arbitrarily connected interaction graphs. Our gate relies on onetimeoptimized adiabatic laser pulses and is fully programmable by adjusting two holdtimes during operation. We numerically demonstrate an implementation of the quantum approximate optimization algorithm (QAOA) for a small scale test problem. Our approach allows for efficient execution of variational optimization steps with a constant number of system manipulations, independent of the system size, thus paving the way for experimental investigations of QAOA beyond the reach of numerical simulations.

S. Hollerith, S. Srakaew, D. Wei, A. Rubio López, D. Adler, P. Weckesser, A. Kruckenhauser, V. Walther, R. van Bijnen, J. Rui, C. Gross, I. Bloch, J. Zeiher Realizing distanceselective interactions in a Rydbergdressed atom array,
Phys. Rev. Lett. 128 113602 (20220314),
http://dx.doi.org/10.1103/PhysRevLett.128.113602 doi:10.1103/PhysRevLett.128.113602 (ID: 720748)
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Measurementbased quantum computing relies on the rapid creation of largescale entanglement in a register of stable qubits. Atomic arrays are well suited to store quantum information, and entanglement can be created using highlyexcited Rydberg states. Typically, isolating pairs during gate operation is difficult because Rydberg interactions feature long tails at large distances. Here, we engineer distanceselective interactions that are strongly peaked in distance through offresonant laser coupling of molecular potentials between Rydberg atom pairs. Employing quantum gas microscopy, we verify the dressed interactions by observing correlated phase evolution using manybody Ramsey interferometry. We identify atom loss and coupling to continuum modes as a limitation of our present scheme and outline paths to mitigate these effects, paving the way towards the creation of largescale entanglement.