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Chinese Physics B

Implementation of quantum phase gate between two atoms via Rydberg antiblockade and adiabatic passage

Xi Tan, Jin‐Lei Wu, Can Deng, Wei-Jian Mao, Haitao Wang, Xin Ji

Published Oct 1, 2018• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/27/10/100307

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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 propose several schemes for implementing a two-qubit quantum phase gate between two Rydberg atoms. The schemes could be realized in one step without adiabatic passage which depends on the specifical shapes and tailored pulse sequences of the laser fields. When the Rydberg-Rydberg-interaction (RRI) strength and the parameters of the driving fields satisfy some certain conditions, the effective Rabi oscillation between the two-excitation Rydberg state and the ground state would be generated, which is out of the Rydberg blockade regime and essential for our scheme. In addition, the individual addressing of the atoms is not required. And the schemes can work under strong or weak RRI strength. The imperfections induced by the variation of RRI strength and spontaneous emission are discussed through solving the master equation numerically.
We propose a controlled-Z gate scheme for Rydberg atoms based on level-crossing-free echoing rapid adiabatic population transfer. We design antisymmetric Rabi frequency pulses and symmetric detuning pulses, enabling the system to completely avoid level-crossing points throughout the evolution, and the dynamical phase is naturally eliminated by the time-reversal symmetry of the double-pulse sequence. We incorporate dissipative effects through the Lindblad master equation. The numerical simulation yields a two-qubit CZ gate fidelity of 0.9999. When the Rabi-frequency fluctuation is within ±2%\pm 2\%±2%, and the detuning offset is within ±1%\pm 1\%±1%, the fidelity can still remain above 0.999. Under the same dissipative model, the three-qubit CCZ gate achieves a fidelity of 0.999. When a single-parameter fluctuation does not exceed ±3%\pm 3\%±3%, the fidelity is always higher than 0.997. Our scheme requires no laser phase jumps or fast switching operations. The zero-area pulse structure suppresses first-order intensity noise, and the symmetric double-pulse sequence avoids spatially resolved laser switching, making it suitable for parallel gate operations in large-scale neutral-atom arrays.
We show that with adiabatic passage, one can reliably drive two-photon optical transitions between the ground states and interacting Rydberg states in a pair of atoms. For finite Rydberg-interaction strengths an adiabatic pathway towards the doubly Rydberg excited state is identified when a constant detuning is applied with respect to an intermediate optically excited level. The Rydberg interaction among the excited atoms provides a phase that may be used to implement quantum gate operations on atomic ground-state qubits.
We show that with adiabatic passage, one can reliably drive two-photon optical transitions between the ground states and interacting Rydberg states in a pair of atoms. For finite Rydberg interaction strengths a new adiabatic pathway towards the doubly Rydberg excited state is identified when a constant detuning is applied with respect to an intermediate optically excited level. The Rydberg interaction among the excited atoms provides a phase that may be used to implement quantum gate operations on atomic ground state qubits.
The Rydberg blockade mechanism is now routinely considered for entangling qubits encoded in clock states of neutral atoms. Challenges towards implementing entangling gates with high fidelity include errors due to thermal motion of atoms, laser amplitude inhomogeneities, and imperfect Rydberg blockade. We show that adiabatic rapid passage by Rydberg dressing provides a mechanism for implementing two-qubit entangling gates by accumulating phases that are robust to these imperfections. We find that the typical error in implementing a two-qubit gate, such as the controlled phase gate, is dominated by errors in the single-atom light shift, and that this can be easily corrected using adiabatic dressing interleaved with a simple spin echo sequence. This results in a two-qubit M\o{}lmer-S\o{}rensen gate. A gate fidelity $\ensuremath{\sim}0.995$ is achievable with modest experimental parameters and a path to higher fidelities is possible for Rydberg states in atoms with a stronger blockade, longer lifetimes, and larger Rabi frequencies.
We propose a mechanism of ground-state blockade between two NNN-type Rydberg atoms by virtue of the Rydberg-antiblockade effect and the Raman transition. Inspired by the quantum Zeno effect, the strong Rydberg antiblockade interaction plays a role in frequently measuring one ground state of two, leading to a blockade effect for double occupation of the corresponding quantum state. By encoding the logic qubits into the ground states, we efficiently avoid the spontaneous emission of the excited Rydberg state and maintain the nonlinear Rydberg-Rydberg interaction at the same time. As applications, we discuss in detail the feasibility of preparing two-atom and three-atom entanglement with ground-state blockade in closed and open systems, respectively, which shows that a high fidelity of the entangled state can be obtained with current experimental parameters.