Rydberg atoms with principal quantum number n >> 1 have exaggerated atomic properties including dipole-dipole interactions that scale as n^4 and radiative lifetimes that scale as n^3. It was proposed a decade ago to take advantage of these properties to implement quantum gates between neutral atom qubits. The availability of a strong, long-range interaction that can be coherently turned on and off is an enabling resource for a wide range of quantum information tasks stretching far beyond the original gate proposal. Rydberg enabled capabilities include long-range two-qubit gates, collective encoding of multi-qubit registers, implementation of robust light-atom quantum interfaces, and the potential for simulating quantum many body physics. We review the advances of the last decade, covering both theoretical and experimental aspects of Rydberg mediated quantum information processing.Comment: accepted version, to appear in Rev. Mod. Phys., 40 figures

Blockade interactions whereby a single particle prevents the flow or excitation of other particles provide a mechanism for control of quantum states, including entanglement of two or more particles. Blockade has been observed for electrons 1-3 , photons 4 and cold atoms 5 . Furthermore, dipolar interactions between highly excited atoms have been proposed as a mechanism for 'Rydberg blockade' 6,7 , which might provide a novel approach to a number of quantum protocols [8][9][10][11] . Dipolar interactions between Rydberg atoms were observed several decades ago 12 and have been studied recently in a many-body regime using cold atoms [13][14][15][16][17][18] . However, to harness Rydberg blockade for controlled quantum dynamics, it is necessary to achieve strong interactions between single pairs of atoms. Here, we demonstrate that a single Rydberg-excited rubidium atom blocks excitation of a second atom located more than 10 µm away. The observed probability of double excitation is less than 20%, consistent with a theoretical model of the Rydberg interaction augmented by Monte Carlo simulations that account for experimental imperfections.The mechanism of Rydberg blockade is shown in Fig. 1a. Two atoms, one labelled 'control' and the other 'target', are placed in proximity with each other. The ground state |1 and Rydberg state |r of each atom form a two-level system that is coupled by laser beams with Rabi frequency Ω . Application of a 2π pulse (Ωt = 2π with t being the pulse duration) on the target atom results in excitation and de-excitation of the target atom giving a phase shift of π on the quantum state, |1 t → −|1 t . If the control atom is excited to the Rydberg state before application of the 2π pulse, the dipole-dipole interaction |r c ↔ |r t shifts the Rydberg level by an amount B that detunes the excitation of the target atom so that it is blocked and |1 t → |1 t . Thus, the excitation dynamics and phase of the target atom depend on the state of the control atom. Combining this Rydberg-blockade-mediated controlled-phase operation 6 with π/2 single-atom rotations between states |0 t and |1 t of the target will implement the CNOT gate between two atoms. We have previously demonstrated the ability to carry out ground-state rotations at individual trapping sites 19 , as well as coherent excitation from ground to Rydberg states at a single site 20 . Here, we describe experiments that demonstrate the Rydberg blockade effect between two neutral atoms separated by more than 10 µm, which is an enabling step towards creation of entangled atomic states. Previous demonstrations of neutral-atom entanglement have relied on shortrange collisions at length scales characterized by a low-energy scattering length of about 10 nm (refs 21,22). Our results, using laser-cooled and optically trapped 87 Rb, extend the distance for strong two-atom interactions by three orders of magnitude, and place us in a regime where the interaction distance is large compared with 1 µm, which is the characteristic wavelength of light needed for...

We present the first demonstration of a CNOT gate between two individually addressed neutral atoms. Our implementation of the CNOT uses Rydberg blockade interactions between neutral atoms held in optical traps separated by >8 microm. Using two different gate protocols we measure CNOT fidelities of F=0.73 and 0.72 based on truth table probabilities. The gate was used to generate Bell states with fidelity F=0.48+/-0.06. After correcting for atom loss we obtain an a posteriori entanglement fidelity of F=0.58.

We present a review of quantum computation with neutral atom qubits. After an overview of architectural options and approaches to preparing large qubit arrays we examine Rydberg mediated gate protocols and fidelity for two-and multi-qubit interactions. Quantum simulation and Rydberg dressing are alternatives to circuit based quantum computing for exploring many body quantum dynamics. We review the properties of the dressing interaction and provide a quantitative figure of merit for the complexity of the coherent dynamics that can be accessed with dressing. We conclude with a summary of the current status and an outlook for future progress.

We analyze the effects of Zeeman degeneracies on the long-range interactions between like Rydberg atoms, with particular emphasis on applications to quantum information processing using van der Waals blockade. We present a general analysis of how degeneracies affect the primary error sources in blockade experiments, emphasizing that blockade errors are sensitive primarily to the weakest possible atom-atom interactions between the degenerate states, not the mean interaction strength. We present explicit calculations of the van der Waals potentials in the limit where the fine-structure interaction is large compared to the atom-atom interactions. The results are presented for all potential angular momentum channels invoving s, p, and d states. For most channels there are one or more combinations of Zeeman levels that have extremely small dipole-dipole interactions and are therefore poor candidates for effective blockade experiments. Channels with promising properties are identified and discussed. We also present numerical calculations of Rb and Cs dipole matrix elements and relevant energy levels using quantum defect theory, allowing for convenient quantitative estimates of the van der Waals interactions to be made for principal quantum numbers up to 100. Finally, we combine the blockade and van der Waals results to quantitatively analyze the angular distribution of the blockade shift and its consequence for angular momentum channels and geometries of particular interest for blockade experiments with Rb.

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We characterize single qubit Clifford gate operations with randomized benchmarking in a 2D array of neutral atom qubits, and demonstrate global and site selected gates with high fidelity. An average fidelity of F 2 = 0.9983( 14) is measured for global microwave driven gates applied to a 49 qubit array. Single site gates are implemented with a focused laser beam to Stark shift the microwaves into resonance at a selected site. At Stark selected single sites we observe F 2 = 0.9923(7) and an average spin flip crosstalk error at other sites of 0.002(9).

We present experimental results on two-qubit Rydberg blockade quantum gates and entanglement in a two-dimensional qubit array. Without post selection against atom loss we achieve a Bell state fidelity of 0.73±0.05, the highest value reported to date. The experiments are performed in an array of single Cs atom qubits with a site to site spacing of 3.8 µm. Using the standard protocol for a Rydberg blockade CZ gate together with single qubit operations we create Bell states and measure their fidelity using parity oscillations. We analyze the role of AC Stark shifts that occur when using two-photon Rydberg excitation and show how to tune experimental conditions for optimal gate fidelity.