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Physical Review A

Nonadiabatic holonomic quantum computation using Rydberg blockade

Yi‐Hao Kang, Ye‐Hong Chen, Zhi‐Cheng Shi, Bi‐Hua Huang, Jie Song, Yan Xia

Published Apr 23, 2018• 77 citations
Publisher

Abstract

In this paper, we propose a scheme for realizing nonadiabatic holonomic computation assisted by two atoms and the shortcuts to adiabaticity (STA). The blockade effect induced by strong Rydberg-mediated interaction between two Rydberg atoms provides us the possibility to simplify the dynamics of the system, and the STA helps us design pulses for implementing the holonomic computation with high fidelity. Numerical simulations show the scheme is noise immune and decoherence resistant. Therefore, the current scheme may provide some useful perspectives for realizing nonadiabatic holonomic computation.

DOI
10.1103/physreva.97.042336

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In this paper, we propose a scheme for realizing nonadiabatic holonomic computation assisted by two atoms and the shortcuts to adiabaticity (STA). The blockade effect induced by strong Rydberg-mediated interaction between two Rydberg atoms provides us the possibility to simplify the dynamics of the system, and the STA helps us design pulses for implementing the holonomic computation with high fidelity. Numerical simulations show the scheme is noise immune and decoherence resistant. Therefore, the current scheme may provide some useful perspectives for realizing nonadiabatic holonomic computation.
We propose a protocol to realize atomic nonadiabatic holonomic quantum computation (NHQC) with two computational atoms and an auxiliary atom. Dynamics of the system is analyzed in the regime of Rydberg blockade, and robust laser pulses are designed via reverse engineering, so that quantum gates can be easily realized with hig h fidelities. In addition, we also study the evolution suffering from dissipation with a master equation. The result indicates that decays of atoms can be heralded by measuring the state of the auxiliary atom, and nearly perfect unitary evolution can be obtained if the auxiliary atom remains in its Rydberg state. Therefore, the protocol may be helpful to realize NHQC in a dissipative environment.
In this paper, we propose a scheme for implementing the nonadiabatic holonomic quantum computation (NHQC+) of two Rydberg atoms by using invariant-based reverse engineering (IBRE). The scheme is based on Förster resonance induced by strong dipole-dipole interaction between two Rydberg atoms, which provides a selective coupling mechanism to simply the dynamics of system. Moreover, for improving the fidelity of the scheme, the optimal control method is introduced to enhance the gate robustness against systematic errors. Numerical simulations show the scheme is robust against the random noise in control fields, the deviation of dipole-dipole interaction, the Förster defect, and the spontaneous emission of atoms. Therefore, the scheme may provide some useful perspectives for the realization of quantum computation with Rydberg atoms.
In this paper, we propose a scheme for implementing the nonadiabatic holonomic quantum computation (NHQC+) of two Rydberg atoms by using invariant-based reverse engineering (IBRE). The scheme is based on Förster resonance induced by strong dipole-dipole interaction between two Rydberg atoms, which provides a selective coupling mechanism to simply the dynamics of system. Moreover, for improving the fidelity of the scheme, the optimal control method is introduced to enhance the gate robustness against systematic errors. Numerical simulations show the scheme is robust against the random noise in control fields, the deviation of dipole-dipole interaction, the Förster defect, and the spontaneous emission of atoms. Therefore, the scheme may provide some useful perspectives for the realization of quantum computation with Rydberg atoms.
Abstract We propose a scheme for realizing nonadiabatic holonomic quantum computation within a decoherence-free subspace using Rydberg atoms. By employing large-detuned lasers and the Rydberg antiblockade condition, we construct an effective Hamiltonian that couples logical states in a three-atom decoherence-free subspace while ensuring that the Rydberg states remain unpopulated. This approach significantly suppresses decoherence caused by atomic spontaneous emission and mitigates the mechanical effects and sensitivity to interatomic distance variations associated with Rydberg excitations. We demonstrate the realization of both conventional and single-loop single-logical-qubit holonomic gates with high fidelity. Furthermore, by utilizing an asymmetric encoding method, in which the control logical qubits employ Rydberg-state encoding to provide the required conditional blockade, we extend the scheme to construct universal two- and three-logical-qubit holonomic gates, offering a robust and scalable approach for quantum information processing.
Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors as well as high-speed realization. Several schemes of its implementation have been put forward based on various physical systems, each of which has some particular merits. In this paper, we put forward an alternative scheme of nonadiabatic holonomic quantum computation, in which a universal set of quantum gates is realized based on Rydberg superatoms. A Rydberg superatom is a mesoscopic atomic ensemble that allows for only a single Rydberg excitation shared by many atoms within a blockade radius and can be used to generate the collective states to encode the qubits. In our scheme, the qubit is encoded into two collective ground states of Rydberg superatoms and the interaction between two long-range Rydberg superatoms is mediated by a microwave cavity with the aid of two additional collective Rydberg states. Different from the previous schemes, which are based on the systems in the microscope scale, the present scheme is based on atomic ensembles in the mesoscopic scale. Besides the common merits of nonadiabatic holonomic quantum computation such as the robustness and the speediness, the Rydberg-superatom-based scheme has the following particular merits: the long coherence time of Rydberg states and the operability of the mesoscopic systems.
In this paper, we propose a one-step scheme for implementing the nonadiabatic holonomic swap gate with Rydberg atoms. By applying invariant-based reverse engineering to design the effective Hamiltonian of the system, a suitable evolution path for implementing nonadiabatic holonomic quantum computation is found. In addition, the systematic-error-sensitivity nullified optimal control method is considered in the parameter selections, so that the scheme is insensitive to the systematic error of pulses. We also estimate the effects of random noise, the random initial phase of the pulses, the Doppler shift, and decoherence on the scheme. The numerical results show that the scheme exhibits fairly good performance against these negative factors. Finally, we generalize the scheme to realize the non-Clifford swap gates. Therefore, this scheme can provide a feasible framework for implementing high-fidelity and robust swap gates and non-Clifford swap gates with Rydberg atoms.