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Laser Physics Letters

One-step implementation of multiqubit controlled–controlled-Z gates with Rydberg atoms

Yan Li, Zhe-Ping Lin, Xinyu Zhao, Ye‐Hong Chen, Yan Xia

Published Jul 21, 2023• 0 citations
Publisher

Abstract

Abstract In this paper, we propose a one-step scheme for generating a multiqubit controlled–controlled-Z (CCZ) gate based on Rydberg atoms where an amplitude-modulated field is employed to induce Rydberg antiblockade. The Rydberg atoms can form a Rabi oscillation between the ground state and the collective excited state effectively, so a one-step three-qubit CCZ gate can be easily achieved through a Rabi cycle. Numerical simulation results show that the scheme has a high fidelity and robustness against errors which are caused by parameter errors, intrinsic errors, and atomic decays. Therefore, we hope that this scheme will enable fast and robust quantum computing in the near future.

DOI
10.1088/1612-202x/ace70b

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Abstract In this paper, we propose a one-step scheme for generating a multiqubit controlled–controlled-Z (CCZ) gate based on Rydberg atoms where an amplitude-modulated field is employed to induce Rydberg antiblockade. The Rydberg atoms can form a Rabi oscillation between the ground state and the collective excited state effectively, so a one-step three-qubit CCZ gate can be easily achieved through a Rabi cycle. Numerical simulation results show that the scheme has a high fidelity and robustness against errors which are caused by parameter errors, intrinsic errors, and atomic decays. Therefore, we hope that this scheme will enable fast and robust quantum computing in the near future.
Although the three-body Rydberg antiblockade regime (RABR) can produce Rabi oscillation between the Rydberg collective excited state and the collective ground state, it is still hard to use the RABR to construct the three-qubit quantum logic gate in one step since the effective Hamiltonian is always accompanied by undesired Stark shifts. In order to overcome this difficulty, an additional laser is introduced to eliminate the Stark shifts in the ground-state subspace. And the initial RABR condition is modified to eliminate the remaining undesired Stark shifts in the collective-excitation subspace. The modified RABR is then generalized to the n(n>3)n (n>3)n(n>3)-qubit case. Based on the proposed regime, one-step schemes to construct three- and nnn-qubit quantum controlled-PHASE gates are proposed without the requirement of atomic addressability. The asymmetric Rydberg-Rydberg interaction, which is more practical for Rydberg atoms, is also discussed and proven to be feasible for the modified RABR and quantum controlled-PHASE gate in theory. A full-Hamiltonian-based master equation is used to evaluate the performance and some experimental parameters are also considered.
With a resonant amplitude-modulation field on two Rydberg atoms, we propose a Rydberg antiblockade (RAB) regime, where the Rabi oscillation between collective ground and excited states is induced. A controlled-Z gate can be yielded through a Rabi cycle. Further, several common issues of the RAB gates are solved by modifying the parameter relation. The gate fidelity and gate robustness against the control error are enhanced with a shaped pulse. The requirement of control precision of the Rydberg-Rydberg interaction strength is relaxed. In addition, the atomic excitation is restrained and therefore the gate robustness against atomic decay is enhanced.
Fault-tolerant implementation of quantum gates is one of preconditions for realizing quantum computation. The platform of Rydberg atoms is one of the most promising candidates for achieving quantum computation. We propose to implement a controlled-ZZZ gate on Rydberg atoms where an amplitude-modulated field is employed to induce Rydberg antiblockade. Gate robustness against the fluctuations in the Rydberg-Rydberg interaction can be largely enhanced by adjusting amplitude-modulated field. Furthermore, we introduce a Landau-Zener-St\"uckelberg transition on the target atom so as to improve the gate resilience to the deviation in the gate time and the drift in the pulse amplitude. With feasible experimental parameters, one can achieve the gate with low fidelity errors caused by atomic decay, interatomic dipole-dipole force, and Doppler effects. Finally, we generalize the gate scheme into multiqubit cases, where resilient multiqubit phase gates can be obtained in one step with an unchanged gate time as the number of qubits increases.
Multiqubit CCZ gates form one of the building blocks of quantum algorithms and have been involved in achieving many theoretical and experimental triumphs. Designing a simple and efficient multiqubit gate for quantum algorithms is still by no means trivial as the number of qubits increases. Here, by virtue of the Rydberg blockade effect, we propose a scheme to rapidly implement a three-Rydberg-atom CCZ gate via a single Rydberg pulse, and successfully apply the gate to realize the three-qubit refined Deutsch-Jozsa algorithm and three-qubit Grover search. The logical states of the three-qubit gate are encoded to the same ground states to avoid an adverse effect of the atomic spontaneous emission. Furthermore, there is no requirement for individual addressing of atoms in our protocol.
Abstract We present a robust protocol for implementing high-fidelity multiqubit controlled phase gates (C k Z) on neutral atom qubits coupled to highly excited Rydberg states. Our approach is based on extending adiabatic rapid passage to two-photon excitation via a short-lived intermediate excited state common to alkali-atom Rydberg experiments, accounting for the full impact of spontaneous decay and differential AC Stark shifts from the complete manifold of hyperfine excited states. We evaluate and optimise gate performance, concluding that for Cs and currently available laser frequencies and powers, a CCZ gate with fidelity F > 0.995 for three qubits and CCCZ with F > 0.99 for four qubits is attainable in ∼ 1.8 μs via this protocol. Higher fidelities are accessible with future technologies, and our results highlight the utility of neutral atom arrays for the native implementation of multiqubit unitaries.
Controlled-phase (CP) gates with an arbitrary phase, which play an irreplaceable role in quantum computation and quantum information processing, are constructed between two neutral-atom qubits by using the Rydberg antiblockade regime. The phases needed for the CP gates are induced by the collective excitation of the pair of atoms. Numerical simulations show that high-fidelity CP gates can be obtained. In addition, the optimization of the scheme is given to enhance the robustness against the control error. As applications, we study in detail the preparation of n-qubit Knill–Laflamme–Milburn (KLM) states and a cluster state based on the Rydberg CP gates. The high-fidelity KLM states and cluster state can be obtained with the current physical parameters.