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Journal of the Optical Society of America B

Rydberg-atom-based controlled arbitrary-phase gate and its applications

Xiaoyu Zhu, Erjun Liang, Shi‐Lei Su

Published Jun 25, 2019• 11 citations
Publisher

Abstract

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.

DOI
10.1364/josab.36.001937

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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.
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.
Through analyzing the effective dynamics of two Rydberg atoms under the dispersive coupling process, we give a method to modify the traditional antiblockade regime with simultaneous driving without adding any extra controls and resources. The modified regime can be used to construct controlled-PHASE and controlled-NOT gates in one step without manipulating the shape and amplitude, and tailoring sequences of the driving pulses. For the controlled-PHASE gate, only one pumping process from the ground state to the Rydberg state of each atom is required thus the resource is minimal. And the atomic addressability is not necessary. The scheme can be improved a lot after adding single-qubit operations since arbitrary phases can be achieved accurately with a short period of evolution time. For one-step construction of controlled-NOT gate, two schemes with high fidelities are given and discussed. Besides, the modified regime can also be used to improve the performance of the dissipation-based quantum entanglement preparation scheme. The optimal value of the modified condition for entanglement preparation is discussed for a wide range of parameters. Our study enriches the physics and applications of the simultaneous-driving-based Rydberg antiblockade regime without adding any operation complexity.
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.
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.
A specific class of partially entangled states known as Knill-Laflamme-Milburn states (or KLM states) has been proved to be useful in relation to quantum information processing [Knill et al., Nature 409, 46 (2001)]. Although the usage of such states is widely investigated, considerably less effort has been invested into experimentally accessible preparation schemes. This paper discusses the possibility to employ a tunable controlled phase gate to generate an arbitrary Knill-Laflamme-Milburn state. In the first part, the idea of using the controlled phase gate is explained on the case of two-qubit KLM states. Optimization of the proposed scheme is then discussed for the framework of linear optics. Subsequent generalization of the scheme to arbitrary n-qubit KLM state is derived in the second part of this paper.
Individual neutral atoms excited to Rydberg states are a promising platform for quantum simulation and quantum information processing. However, experimental progress to date has been limited by short coherence times and relatively low gate fidelities associated with such Rydberg excitations. We report progress towards high-fidelity quantum control of Rydberg-atom qubits. Enabled by a reduction in laser phase noise, our approach yields a significant improvement in coherence properties of individual qubits. We further show that this high-fidelity control extends to the multi-particle case by preparing a two-atom entangled state with a fidelity exceeding 0.97(3), and extending its lifetime with a two-atom dynamical decoupling protocol. These advances open up new prospects for scalable quantum simulation and quantum computation with neutral atoms.