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Journal of Physics B Atomic Molecular and Optical Physics

Implementing a neutral atom Rydberg gate without populating the Rydberg state

E. Brion, Line Hjortshøj Pedersen, Klaus Mølmer

Published Apr 18, 2007• 32 citations
Publisher

Abstract

In this paper, we propose a neutral atom implementation of the two-qubit conditional phase gate, based on the large Rydberg–Rydberg interaction induced energy shift. Contrary to previous proposals, this gate does not substantially populate the Rydberg levels. After describing the model in detail, we provide numerical simulations and discuss the performance of our gate. In particular we address the influence on the fidelity of spontaneous emission and atomic motion.

DOI
10.1088/0953-4075/40/9/s09

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In this paper, we propose a neutral atom implementation of the two-qubit conditional phase gate, based on the large Rydberg–Rydberg interaction induced energy shift. Contrary to previous proposals, this gate does not substantially populate the Rydberg levels. After describing the model in detail, we provide numerical simulations and discuss the performance of our gate. In particular we address the influence on the fidelity of spontaneous emission and atomic motion.
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 several schemes for implementing a fast two-qubit quantum gate for neutral atoms with the gate operation time much faster than the time scales associated with the external motion of the atoms in the trapping potential. In our example, the large interaction energy required to perform fast gate operations is provided by the dipole-dipole interaction of atoms excited to low-lying Rydberg states in constant electric fields. A detailed analysis of imperfections of the gate operation is given.
Abstract Multi-qubit quantum gates are the most important building blocks for quantum computation. In this article, we propose a scheme for realizing the Toffoli gate in a linear neutral atom array. Two ground-state hyperfine levels of the atoms are considered as qubit states. Our method relies on the strong and long-range interactions between atoms due to Rydberg excitations and the occurrence of dark states in the target qubit, with both control and target qubits being individually addressed with laser pulses. Our gate protocol enables precise control over the quantum states of individual qubits, effectively suppressing undesirable transitions to ensure high-fidelity gate performance. We also implement two-atom Rydberg antiblockade mechanism to avoid any unwanted population blockage in the control atoms to get the best fidelity. At zero temperature, the gate fidelity is estimated to be about 99.16% for realistic laser power omitting the motional state of the atoms when the interatomic distance ( l ) 6.55 μ m. We construct a C n NOT gate with n > 2 in a 2D atomic array by exploiting the n -atom Rydberg antiblockade (RAB) mechanism, which allows n atoms within the blockade radius to be simultaneously excited to the Rydberg states. In particular, we simulate C 3 NOT gate with about 98.37 % fidelity. We further analyze the gate error by decreasing the interatomic distance and find that gate fidelity improves more rapidly for larger n with increased interaction potential. We find that more than 99 % fidelity can be achieved for C 3 NOT gate for l < 6.2 μ m, implying that our proposed scheme promising and reliable for multi-qubit controlled NOT gates. For a finite temperature ( ∼ 30 μ K), including the Doppler dephasing, we simulate our gates to achieve 98.90% and 98.54 % fidelity for the Toffoli gate and C 3
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.
The quantum swap gate is one of the most useful gates for quantum computation. Two-qubit entanglement and a controlled-NOT quantum gate in a neutral Rydberg atom system have been achieved in recent experiments. It is therefore very interesting to propose a scheme here for swapping a quantum state between two trapped neutral atoms via the Rydberg blockade mechanism. The atoms interact with a sequence of laser pulses without individual addressing. The errors of the swap gate due to imprecision of pulse length, finite Rydberg interaction, and atomic spontaneous emission are discussed.