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We explore the protection of quantum gates from arbitrary single- and two-qubit noises with properly designed dynamical decoupling pulses. The proposed dynamical decoupling method is a concatenation of a sequence of pulses formed by $\sigma_x$, $\sigma_x\sigma_x$ with another sequence constructed by $\sigma_z$, $\sigma_z\sigma_z$. The concatenation of the two sequences results in desired pulses to fight agianst any single- and two-qubit errors. The success of our method relies on the ability to adjust system parameters or interaction terms, which can be achieved in different physical systems, including trapped ions and superconducting qubits. We finally explore the performance of our method numerically with the above-mentioned errors that are changing at any moment and show the preferred protection offered by the method. Therefore, our method is a timely step forward in preserving quantum gates at the level of physical qubits., Comment: 5 pages

In the preceding Comment [1] it was claimed that the third-order Hamiltonian obtained in our original paper [2] is not Hermitian for general situations when considering time-dependence and the way of deriving the effective third-order expansion is not very rigorous. To reply the comment we should emphasize the following three points: first of all, the third-order Hamiltonian given in our paper is exactly Hermitian under the conditions mentioned there. Secondly, the iterative method adopted in our paper to derive the generalized effective Hamiltonian is equivalent to the Dyson series, and its correctness can thus be guaranteed. Thirdly, although the truncated effective Hamiltonian is indeed non-Hermitian under the time-dependent situation as presented in the Comment, it corresponds exactly to the non-unitary truncated Dyson series. Considering the truncated Dyson series has been extensively utilized in the time-dependent perturbation theory, in our opinion, the non-Hermitian truncated effective Hamiltonian can still be treated as an approximation of the effective Hamiltonian., Comment: 9 pages

We investigate the multi-photon resonance and multi-ion excitation in a single-mode cavity with identical vibrating ion-qubits, which enables the tripartite interaction among the internal states of ions, the cavity mode and the ions' vibrational motion. Under particular resonant conditions, we derive effective Hamiltonians for the three-photon and the three-excitation cases, respectively, and find that the magnitude of the effective coupling energy can be tuned through the vibration mode, allowing for manipulations of ion-photon coupling in experiments. Furthermore, we analyze the system dynamics of our proposed setups and demonstrate the Rabi oscillation behaviors in these systems with dissipation effects. We propose our system as a versatile platform for the exploration of entangled multi-qubit physics., Comment: 25 pages, 18 figures

We explore the implementation of hybridly protected quantum operations combining the merits of holonomy, dynamical decoupling approach and dephasing-free feature based on a simple and experimentally achievable spin model. The implementation of the quantum operations can be achieved in different physical systems with controllable parameters. The protected quantum operations are hence controllable, well-suited for resolving various quantum computation tasks, such as executing quantum error-correction codes or quantum error mitigation. Our scheme is based on experimentally achievable Hamiltonian with reduced requirement of computational resources and thus, it brings us closer towards realizing protected quantum operations for resolving quantum computation tasks in near-term quantum devices., Comment: 5 pages, 1 figure

We propose a scheme for entanglement distribution among different single atoms trapped in separated cavities. In our scheme, by reflecting an input coherent optical pulse from a cavity with a single trapped atom, a controlled phase-shift gate between the atom and the coherent optical pulse is achieved. Based on this gate and homodyne detection, we construct an $n$-qubit parity gate and show its use for distribution of a large class of entangled states in one shot, including the GHZ state $\left\vert GHZ_{n}\right\rangle $, W state $\left\vert W_{n}\right\rangle $, Dicke state $\left\vert D_{n,k}\right\rangle $ and certain sums of Dicke states $% \left\vert G_{n,k}\right\rangle $. We also show such distribution could be performed with high success probability and high fidelity even in the presence of channel loss., Comment: 8 pages, 6 figures

James' effective Hamiltonian method has been extensively adopted to investigate largely detuned interacting quantum systems. This method is just corresponding to the second-order perturbation theory, and cannot be exploited to treat the problems which should be solved by using the third or higher-order perturbation theory. In this paper, we generalize James' effective Hamiltonian method to the higher-order case. Using the method developed here, we reexamine two examples published recently [Phys. Rev.Lett. 117, 043601 (2016), Phys. Rev A 92, 023842 (2015)], our results turn out to be the same as the original ones derived from the third-order perturbation theory and adiabatic elimination method respectively. For some specific problems, this method can simplify the calculating procedure, and the resultant effective Hamiltonian is more general., Comment: 5 pages, no figure, submitted to Phys. Rev. A

In this work, the absorption spectrum of a two-level ion in a linear Paul trap is investigated, the ion is supposed to be driven by two orthogonal laser beams, the one along the axial of the trap acts as the control light beam, the other as probe beam. When the frequency of the control laser is tuned to the first red sideband of the ionic transition, the coupling between the internal states of the ion and vibrational mode turns out to be a Jaynes-Cummings (JC) Hamiltonian, which together with the coupling between the probe beam and the two-level ion constructs a {\Lambda}-type three-level structure. In this case the transparency window may appear in the absorption spectrum of the probe light, which is induced by the ionic vibration and is very similar to the cavity induced transparency [1996 Opt. Commun. 126 230-235]. On the other hand, when the frequency of the control laser is tuned to the first blue sideband of the ionic transition, the two-level ion and vibrational mode are governed by an anti-Jaynes-Cummings (anti-JC) Hamiltonian, the total system including the probe beam forms a V -type threelevel structure. And the Autler-Townes splitting in the absorption spectrum is found., Comment: 6 pages, 3 figures, accepted for publication by Laser Physics Letters

We numerically study the propagation of a few-cycle pulse carrying orbital angular momentum (OAM) through a dense atomic system. Nonlinear precursors consisting of high-order vortex har- monics are generated in the transmitted field due to ultrafast Bloch oscillation. The nonlinear precursors survive to propagation effects and are well separated with the main pulse, which provide a straightforward way of measuring precursors. By the virtue of carrying high-order OAM, the obtained vortex precursors as information carriers have potential applications in optical informa- tion and communication fields where controllable loss, large information-carrying capacity and high speed communication are required.

The existence of minimal length scale has motivated the proposal of generalized uncertainty principle, which provides a potential routine to probe quantum gravitational effects in low-energy quantum mechanics experiment. Hitherto, the tabletop experiment of testing deviations from ordinary quantum mechanics are mostly based on microscopic objects. However, the feasibility of these studies are challenged by the recent study of spacetime quantization for composite macroscopic body. In this paper, we propose a scheme to probe quantum gravity effects by revealing the deviations from predictions of Heisenberg uncertainty principle. Our scheme focus on manipulating the interaction sequences between external laser fields and a single trapped ion to seek evidence of spacetime quantization, therefore reduce the complicity induced by large bodies to some extent. The relevant study for microscopic particles is crucial considering the lack of satisfactory theories regarding basic properties for multi-particles in the framework of quantum gravity. Meanwhile, we are managed to set a new upper limit for deformation parameter.

Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of $\frac{N-2}{N}$. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities., Comment: 2 figures; accepted by Sci. Rep