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Chinese Physics Letters

Two-Qubit Geometric Gates Based on Ground-State Blockade of Rydberg Atoms

Ji-Ze Xu, Li-Na Sun, J.-F. Wei, Yan-Xiong Du, Ronghui Luo, L.-L. Yan, Mang Feng, Shi‐Lei Su

Published Aug 1, 2022• 12 citations
Publisher

Abstract

We achieve the robust nonadiabatic holonomic two-qubit controlled gate in one step based on the ground-state blockade mechanism between two Rydberg atoms. By using the Rydberg-blockade effect and the Raman transition mechanism, we can produce the blockade effect of double occupation of the corresponding ground state, i.e., ground-state blockade, to encode the computational subspace into the ground state, thus effectively avoiding the spontaneous emission of the excited Rydberg state. On the other hand, the feature of geometric quantum computation independent of the evolutionary details makes the scheme robust to control errors. In this way, the controlled quantum gate constructed by our scheme not only greatly reduces the gate infidelity caused by spontaneous emission but is also robust to control errors.

DOI
10.1088/0256-307x/39/9/090301

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We achieve the robust nonadiabatic holonomic two-qubit controlled gate in one step based on the ground-state blockade mechanism between two Rydberg atoms. By using the Rydberg-blockade effect and the Raman transition mechanism, we can produce the blockade effect of double occupation of the corresponding ground state, i.e., ground-state blockade, to encode the computational subspace into the ground state, thus effectively avoiding the spontaneous emission of the excited Rydberg state. On the other hand, the feature of geometric quantum computation independent of the evolutionary details makes the scheme robust to control errors. In this way, the controlled quantum gate constructed by our scheme not only greatly reduces the gate infidelity caused by spontaneous emission but is also robust to control errors.
Quantum gates are crucial for quantum computation and quantum information processing. However, their effectiveness is often hindered by systematic errors and decoherence. Therefore, achieving resilient quantum gates to these factors is of great significance. We present a method to construct nonadiabatic holonomic single- and two-qubit gates in a Rydberg ground-state-blockade regime. Our approach utilizes a far-off-resonant technique for the single-qubit gate and a modified Rydberg antiblockade for the two-qubit gate. The reduction of the population of single- and two-excitation Rydberg states and the nonadiabatic holonomic process during the construction of the gates ensure robustness to decoherence and systematic errors, respectively. Numerical results demonstrate the fidelity and robustness of our scheme. The proposed scheme holds promise for future applications in quantum computation and quantum information processing tasks.
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.
In the context of Rydberg anti-blockade, this paper proposes a new scheme for a high-fidelity controlled-unitary gate based on non-adiabatic holonomic quantum computation. Under specific detuning and interaction conditions, the scheme achieves a suitable evolution path for non-adiabatic holonomic quantum computation through reverse engineering of pulse parameters. This scheme can implement arbitrary two-qubit controlled gates with favorable robustness. We also evaluate the effects of spontaneous emission and laser intensity errors on the fidelity; numerical simulations show that the geometric gate scheme still exhibits excellent performance under these errors. Furthermore, we extend the scheme to non-local gates via entanglement transfer and quantum teleportation techniques, and demonstrate its application in the mutual conversion among four-qubit entangled states (GHZ, cluster, and W states). This finding indicates the potential applicability of our scheme to complex quantum information processing tasks.
We propose a nontrivial two-qubit gate scheme in which Rydberg atoms are subject to designed pulses resulting from geometric evolution processes. By utilizing hybrid robust nonadiabatic and adiabatic geometric operations on the control atom and target atom, respectively, we improve the robustness of the two-qubit Rydberg gate against Rabi control errors as well as blockade errors in comparison with the conventional two-qubit blockade gate. Numerical results with the current state-of-the-art experimental parameters corroborates the above mentioned robustness. We also evaluate the influence induced by the motion-induced dephasing and the dipole-dipole interaction and imperfection-excitation-induced leakage errors, which both could decrease the gate fidelity. Our scheme provides a promising route towards systematic control error (Rabi error) as well as blockade-error-resilient geometric quantum computation on neutral atom system.
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.
Nonadiabatic holonomic quantum gates are high-speed and robust. Nevertheless, they were found to be more fragile than the adiabatic gates when systematic errors become dominant. Inspired by the dark-path scheme that was used to partially relieve the systematic error in the absence of external noise, we construct a universal set of nonadiabatic holonomic NNN-qubit gates using the Rydberg-Rydberg interaction between atoms under off-resonant driving. Based on an effective four-level configuration in the Rydberg-atom system, the modified nonadiabatic holonomic geometric gates present a clear resilience to both systematic error in the whole parametric range and external noise. In our scheme, the conventional ultrastrong interaction between control atoms and the target atom for the nonadiabatic holonomic quantum computation is compensated by the detuning of the driving fields on the target atom. That idea yields a deeper understanding about the holonomic transformation. Moreover, our scheme is compact and scale-free with respect to NNN. It is interesting to find that the three-qubit gate is less susceptible to errors than the double-qubit one.