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arXiv:1111.6083 · Physical Review A

Implementation of an experimentally feasible controlled-phase gate on two blockaded Rydberg atoms

Matthias M. Müller, Michael Murphy, Simone Montangero, Tommaso Calarco, Philippe Grangier, Antoine Browaeys

Published Mar 28, 2014• 81 citations
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Abstract

We investigate the implementation of a controlled-$Z$ gate on a pair of Rydberg atoms in spatially separated dipole traps where the joint excitation of both atoms into the Rydberg level is strongly suppressed (the Rydberg blockade). We follow the adiabatic gate scheme of Jaksch et al. [D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. C\^ot\'e, and M. D. Lukin, Phys. Rev. Lett. 85, 2208 (2000)], where the pair of atoms is coherently excited using lasers, and apply it to the experimental setup outlined by Ga\"etan et al. [A. Ga\"etan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, Nat. Phys. 5, 115 (2009)]. We apply optimization to the experimental parameters to improve gate fidelity and consider the impact of several experimental constraints on the gate success.

DOI
10.1103/physreva.89.032334

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We investigate the implementation of a controlled-ZZZ gate on a pair of Rydberg atoms in spatially separated dipole traps where the joint excitation of both atoms into the Rydberg level is strongly suppressed (the Rydberg blockade). We follow the adiabatic gate scheme of Jaksch et al. [D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. C^ot'e, and M. D. Lukin, Phys. Rev. Lett. 85, 2208 (2000)], where the pair of atoms is coherently excited using lasers, and apply it to the experimental setup outlined by Ga"etan et al. [A. Ga"etan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, Nat. Phys. 5, 115 (2009)]. We apply optimization to the experimental parameters to improve gate fidelity and consider the impact of several experimental constraints on the gate success.
One can implement fast two-qubit entangling gates by exploiting the Rydberg blockade. Although various theoretical schemes have been proposed, experimenters have not yet been able to demonstrate two-atom gates of high fidelity due to experimental constraints. We propose a novel scheme, which only uses a single Rydberg pulse illuminating both atoms, for the construction of neutral-atom controlled-phase gates. In contrast to the existing schemes, our approach is simpler to implement and requires neither individual addressing of atoms nor adiabatic procedures. With parameters estimated based on actual experimental scenarios, a gate fidelity higher than 0.99 is achievable.
We study the implementation of a high fidelity controlled-phase gate in a Rydberg quantum computer. The protocol is based on a symmetric gate with respect to the two qubits as experimentally realized by Levine et al. [Phys. Rev. Lett. 123, 170503 (2019)], but allows for arbitrary pulse shapes with time-dependent detuning. Optimizing the pulse shapes, we introduce laser pulses which shorten the time spent in the Rydberg state by 10% and reduce the leading contribution to the gate infidelity, i.e., the decay from the Rydberg state. Remarkably, this reduction can be achieved for smooth pulses in detuning and smooth turning on of the Rabi frequency as required in any experimental realization. We carefully analyze the influence of fundamental error sources such as the photon recoil and the microscopic interaction potential, as well as the harmonic trapping of the atoms for an experimentally realistic setup based on strontium-88 atoms. We find that an average gate fidelity above 99.9% is possible for a very conservative estimation of experimental parameters.
Arrays of qubits encoded in the ground-state manifold of neutral atoms trapped in optical (or magnetic) lattices appear to be a promising platform for the realization of a scalable quantum computer. Two-qubit conditional gates between nearest-neighbor qubits in the array can be implemented by exploiting the Rydberg blockade mechanism, as was shown by D. Jaksch et al. [Phys. Rev. Lett. 85, 2208 (2000)]. However, the energy shift due to dipole-dipole interactions causing the blockade falls off rapidly with the interatomic distance, and protocols based on direct Rydberg blockade typically fail to operate between atoms separated by more than one lattice site. In this work, we propose an extension of the protocol of Jaksch et al. for controlled-ZZZ and controlled-not gates which works in the general case where the qubits are not nearest neighbors in the array. Our proposal relies on the Rydberg excitation hopping along a chain of ancilla noncoding atoms connecting the qubits on which the gate is to be applied. The dependence of the gate fidelity on the number of ancilla atoms, the blockade strength, and the decay rates of the Rydberg states is investigated. A comparison between our implementation of a distant controlled-not gate and one based on a sequence of nearest-neighbor two-qubit gates is also provided.
Abstract High-fidelity controlled-Z (CZ ) gates are essential and mandatory to build a large-scale quantum computer. In neutral atoms, the strong dipole–dipole interactions between their Rydberg states make them one of the pioneering platforms to implement CZ gates. Here we numerically investigate the optimized pulses to generate a high-fidelity Rydberg C Z gate in a three-level ladder-type atomic system. By tuning the temporal shapes of Gaussian or segmented pulses, the populations on the intermediate excited states are shown to be suppressed within the symmetric gate operation protocol, which leads to a C Z gate with a high Bell fidelity up to 99.92 % . These optimized pulses are robust to thermal fluctuations and the excitation field variations. Our results promise a high-fidelity and fast gate operation under amenable and controllable experimental parameters, which goes beyond the adiabatic operation regime under a finite blockade strength.
Combining adiabatic passage and Rydberg antiblockade, we propose a scheme to implement a two-qubit phase gate between two Rydberg atoms. Detuning parameters between frequencies of atomic transitions and those of the corresponding driving lasers are carefully chosen to offset the blockade effect of two Rydberg atoms, so that an effective Hamiltonian, representing a single-photon detuning Λ-type three-level system and concluding the quantum state of two Rydberg atoms excited simultaneously, is obtained. The adiabatic-passage technique, based on the effective Hamiltonian, is adopted to implement a two-atom phase gate by using two time-dependent Rabi frequencies. Numerical simulations indicate that a high-fidelity two-qubit π -phase gate is constructed and its operation time does not have to be controlled accurately. Besides, owing to the long coherence time of the Rydberg state, the phase gate is robust against atomic spontaneous emission.
We study the spatial performance of the entangling gate proposed by H. Levine et al. (Phys. Rev. Lett. 123, 170503 (2019)). This gate is based on a Rydberg blockade technique and consists of just two global laser pulses which drive nearby atoms. We analyze the multilevel Zeeman structure of interacting 87^{87}87Rb Rydberg atoms and model two experimentally available excitation schemes using specific driving beams geometry and polarization. In particular, we estimate the blockade shift dependence on inter-atomic distance and angle with respect to the quantization axis. In addition, we show that using Rydberg ddd-states, in contrast to sss-states, leads to a pronounced angular dependence of the blockade shift and gate fidelity.