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arXiv:2010.14704

Multiple-qubit Rydberg quantum logic gate via dressed-states scheme

Yucheng He, J.M. Liu, F.-Q. Guo, L.-L. Yan, Luo, Ronghui, Erjun Liang, Shi‐Lei Su, Mang Feng

Published Oct 28, 2020• 2 citations
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Abstract

We present a scheme to realize multiple-qubit quantum state transfer and quantum logic gate by combining the advantages of Vitanov-style pulses and dressed-state-based shortcut to adiabaticity (STA) in Rydberg atoms. The robustness of the scheme to spontaneous emission can be achieved by reducing the population of Rydberg excited states through the STA technology. Meanwhile, the control errors can be minimized through using the well-designed pulses. Moreover, the dressed-state method applied in the scheme makes the quantum state transfer more smoothly turned on or off with high fidelity and also faster than traditional shortcut to adiabaticity methods. By using Rydberg antiblockade (RAB) effect, the multiple-qubit Toffoli gate can be constructed under a general selection conditions of the parameters.

DOI
10.48550/arxiv.2010.14704

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We present a scheme to realize multiple-qubit quantum state transfer and quantum logic gate by combining the advantages of Vitanov-style pulses and dressed-state-based shortcut to adiabaticity (STA) in Rydberg atoms. The robustness of the scheme to spontaneous emission can be achieved by reducing the population of Rydberg excited states through the STA technology. Meanwhile, the control errors can be minimized through using the well-designed pulses. Moreover, the dressed-state method applied in the scheme makes the quantum state transfer more smoothly turned on or off with high fidelity and also faster than traditional shortcut to adiabaticity methods. By using Rydberg antiblockade (RAB) effect, the multiple-qubit Toffoli gate can be constructed under a general selection conditions of the parameters.
Multiple-qubit quantum logic gates are an important element in the implementation of quantum computers. The direct construction of multiple-qubit quantum logic gates in an efficient way has important values compared to the construction of multiple-qubit gates using a series of two-qubit and single-qubit gates. We propose a scheme to construct a multiple-qubit CkU{\mathrm{C}}_{k}\mathrm{U}Ck​U gate (kkk denotes the number of control qubits and U means the arbitrary universal operation performed on the target qubit) in a neutral atom platform through the Rydberg blockade effect by successively exciting them to Rydberg states. This scheme takes advantage of the shortcut to adiabaticity of inverse engineering, geometric quantum operations, as well as optimized control theory. The geometric quantum computation considered in this manuscript guarantees the robustness to operational errors. Meanwhile, inverse engineering-based shortcut to adiabaticity provides a further advantage in terms of the speed of the system evolution compared to adiabatic processes. An additional feature of our multiple-qubit quantum logic gate is that arbitrary operation on the target atom can be realized by adjusting the amplitude and phase of the laser fields. Numerical simulation of the master equation based on the full Hamiltonian demonstrates the high fidelity of the proposed scheme and its robustness to operational errors and spontaneous emission.
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
We propose a controlled-PHASE gate for neutral atoms in which one of the qubit state components adiabatically evolves along the multiple-atom eigenstate formed by the chirped laser pulse coupling to Rydberg states and intrinsic dipole-dipole exchange interactions and, consequently, accumulates an interaction-induced geometric phase. The geometric Rydberg gate is not limited by an adiabatic condition, which is sped up by shortcuts to adiabaticity (STA). Analyses show that an STA scheme is more robust than a non-adiabatic case against the variations of control parameters and faster than an adiabatic case, which protects from the decay of Rydberg states. Furthermore, an intermediate value of dipole-dipole interaction strength is enough for our scheme.
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.
Abstract Multiple‐qubit logic gates, as an essential part of quantum logic gates, have wide practical application in quantum computation. Here, a scheme to directly construct a multiple‐qubit logic gate , in which k control atoms apply an universal operation U on each of m target qubits in the Rydberg atom system is proposed. The scheme, based on Rydberg blockade and geometric quantum operations as well as optimized control theory, can greatly reduce the qubit number and the operation steps, improving the speed and robustness of the gating compared to the conventional multiple‐qubit gates consisting of single‐ and two‐qubit gates. Taking the C2U2 gate as an example, the performance of the proposal is numerically evaluated in terms of the fidelity of the quantum gate as well as the robustness against the static systematic errors and spontaneous emission. This work may provide a significative reference for constructing universal multiple‐qubit logic gates in future Rydberg atom experiments.
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.