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arXiv:2008.03059 · Physical Review A

Heralded atomic nonadiabatic holonomic quantum computation with Rydberg blockade

Yi‐Hao Kang, Zhi‐Cheng Shi, Jie Song, Yan Xia

Published Aug 24, 2020• 45 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.102.022617

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arXiv:2107.14486•Jul 30, 2021•0 citations
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 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.
The nonadiabatic holonomic quantum computation (NHQC) has received great attention for decades, however, there are many challenges to its implementation in experiments. To further shorten the evolution time is the first challenge to be conquered to realize high-fidelity quantum gates in NHQC. In this paper, we propose a controlled two-qubit model in Rydberg atoms to realize nonadiabatic holonomic quantum gates, where the evolution time is extremely decreased and the influences of several kinds of noises are minimized by utilizing the time-optimal-control technique on the target atom. In addition, we can construct arbitrary geometric gates by selecting the appropriate parameters in our model. Furthermore, numerical simulations for the $\mathrm{C}\ensuremath{-}T$ gate and $\mathrm{C}\ensuremath{-}\sqrt{H}$ gate based on the master equation show that the fidelities of geometric gates obtained in our model are still very high even though noises are considered, which demonstrates the robustness of our protocol. It is worth noting that the controlled two-qubit model may pave the way to realize fault-tolerant quantum computation in the future.
Nonadiabatic holonomic quantum computation (NHQC) has attracted significant attention due to its fast evolution and the geometric nature-induced resilience to local noises. However, its long operation time and complex physical implementation make it hard to surpass the dynamical scheme, and thus hindering its wide application. Here, we present to implement NHQC with the shortest path under some conditions, through the inverse Hamiltonian engineering technique, which posseses higher fidelity and stronger robustness than previous NHQC schemes. Meanwhile, the gate performance in our scheme can be further improved by using the proposed composite dynamical decoupling pulses, which can efficiently improve both the gate fidelity and robustness, making our scheme outperform the optimal dynamical scheme in a certain parameter range. Remarkably, our scheme can be readily implemented with Rydberg atoms, and a simplified implementation of the controlled-not gate in the Rydberg blockade regime can be achieved. Therefore, our scheme represents a promising progress towards future fault-tolerant quantum computation in atomic systems.
Abstract Nonadiabatic holonomic quantum computation (NHQC) has attracted significant interest due to its intrinsic robustness against local parameter fluctuations. However, conventional NHQC schemes are constrained by long evolution times, with all gate operations requiring the same duration regardless of the rotation angle, leading to increased susceptibility to decoherence. In this paper, we propose a time-optima NHQC (TONHQC) scheme in the Rydberg atomic system, which minimizes gate operation time while maintaining geometric robustness. By solving the quantum brachistochrone equation (QBE), we derive an optimal trajectory for state evolution. We demonstrate the feasibility of TONHQC using87Rb atoms by constructing high-fidelity geometric two-qubit gates. Numerical simulations for controlled-Hadamard (C-H), controlled-π/4 (C-S) and controlled-π/8 (C-T) gates confirm that TONHQC outperforms conventional NHQC protocols, achieving higher fidelity and enhanced resilience against spontaneous emission and Rabi frequency fluctuations. These findings suggest that TONHQC as a promising approach for realizing high-fidelity holonomic quantum gates in Rydberg atom systems, paving the way for scalable and fault-tolerant quantum computation.
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.