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Chinese Physics Letters

Nonadiabatic Holonomic Quantum Computation Based on Rydberg Ground State Blockade

Shi‐Lei Su, Chen 琛 Wang 王, P.-Y. 佩瑶 Song 宋, Gang 刚 Chen 陈

Published Mar 18, 2024• 13 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/41/4/040302

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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.
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.
Nonadiabatic holonomic quantum computation, focusing mainly on implementing universal single- and two-qubit gates, commonly suffers gate fidelity losses inevitably due to the presence of systematic errors. Here we propose to realize fast holonomic multiqubit controlled~(CN_NN​-NOT) Rydberg atom gates. Uniquely, the gate time is independent of the control qubit number NNN. We show that the fast gate is largely immune to laser parameter fluctuations and motional dephasing. The high tolerance of systematic errors can be further enhanced through optimal pulse engineering. The proposed protocol is intrinsically different from typical schemes based on Rydberg blockade or antiblockade, and moreover can be implemented alternatively with superconducting circuits. Our study paves a new way to build robust multiqubit gates with Rydberg atoms trapped in optical arrays or superconducting circuits, and hence contributes to current efforts in developing scalable quantum computation with trapped atoms and fabricable superdonducting devices.
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.
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.
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.