Exploring the properties and applications of topological quantum states is essential to better understand topological matter. Here, we theoretically study a quasi-one-dimensional topological atom array. In the low-energy regime, the atom array is equivalent to a topological superatom. Driving the superatom in a cavity, we study the interaction between light and topological quantum states. We find that the edge states exhibit topology-protected quantum coherence, which can be characterized from the photon transmission. This quantum coherence helps us to find a superradiance-subradiance transition, and we also study its finite-size scaling behavior. The superradiance-subradiance transition also exists in symmetry-breaking systems. More importantly, it is shown that the quantum coherence of the subradiant edge state is robust to random noises, allowing the superatom to work as a topologically protected quantum memory. We suggest a relevant experiment with three-dimensional circuit QED. Our study may have applications in quantum computation and quantum optics based on topological edge states.
Topological effects continue to fascinate physicists since more than three decades. One of their main applications are high-precision measurements of the resistivity. We propose to make also use of the spatially separated edge states. It is possible to realize strongly direction-dependent group velocities. They can also be tuned over orders of magnitude so that robust delay lines and interference devices are within reach.
Majorana zero modes are non-Abelian quasiparticles that emerge on the edges of topological phases of superconductors. Evidence of their presence has been reported in transport measurements on engineered superconducting-based nanostructures. In this manuscript we identify signatures of a topologically protected dynamical manipulation of Majorana zero modes via continuous transport measurement during the manipulation. Specifically, we show that, in a two-terminal geometry, the heat pumped across the terminals at low temperature and voltage bias is characterized by a universal value. We show that…
Single-photon super- and subradiance are important for the quantum memory and quantum information. We investigate one-dimensional atomic arrays under the spatially periodic magnetic field with a tunable phase, which provides a distinctive physics aspect of revealing exotic two-dimensional topological phenomena with a synthetic dimension. A butterfly-like nontrivial bandstructure associated with the non-Hermitian physics involving strong long-range interactions has been discovered. It leads to pairs of topologically-protected edge states, which exhibit the robust super- or subradiance behavior,…
We consider spin chain families inspired by the Su, Schrieffer and Hegger (SSH) model. We demonstrate explicitly the topologically induced spatial localisation of quantum states in our systems. We present detailed investigations of the effects of random noise, showing that these topologically protected states are very robust against this type of perturbation. Systems with such topological robustness are clearly good candidates for quantum information tasks and we discuss some potential applications. Thus, we present interesting spin chain models which show promising applications for quantum de…
We report ab initio calculations showing that a single one-dimensional extended defect can originate topologically-protected metallic states in the bulk of two-dimensional topological insulators. We find that a narrow extended defect composed of periodic units consisting of one octogonal and two pentagonal rings embedded in the hexagonal bulk of a bismuth bilayer introduces two pairs of one-dimensional Dirac-fermion states with opposite spin-momentum locking. Although both Dirac pairs are localized along the extended-defect core, their interactions are screened due to the trivial topological n…
Majorana zero modes are usually attributed to topological superconductors. We study a class of two-dimensional topologically trivial superconductors without chiral edge modes, which nevertheless host robust Majorana zero modes in topological defects. The construction of this minimal single-band model is facilitated by the Hopf map and the Hopf invariant. This work will stimulate investigations of Majorana zero modes in superconductors in the topologically trivial regime.
Topologically protected measurement-based quantum computation on the thermal state of a nearest-neighbor two-body Hamiltonian with spin-3/2 particles
最近，李{ \it et al.} [Phys. Rev. Lett. { \bf 107}，060501（2011）]已经证明，只要温度小于临界值，即阈值温度，就可以在具有自旋2和自旋3/2粒子的最近邻两体哈密顿量的热状态上实现拓扑保护的基于测量的量子计算。在这里，我们表明，热状态的最近邻两体哈密顿量，其中只包括自旋3/2粒子，使我们能够进行拓扑保护的测量为基础的量子计算。阈值温度的计算结果表明，与自旋-2和自旋-3/2系统的阈值温度相当。此外，我们一般表明，一个高连通性的集群状态可以有效地产生从自旋3/2系统的热态没有严重的热噪声积累。
Discrete-time quantum walks allow Floquet topological insulator materials to be explored using controllable systems such as ultracold atoms in optical lattices. By numerical simulations, we study the robustness of topologically protected edge states in the presence of decoherence in one- and two-dimensional discrete-time quantum walks. We also develop a simple analytical model quantifying the robustness of these edge states against either spin or spatial dephasing, predicting an exponential decay of the population of topologically protected edge states. Moreover, we present an experimental pro…
The realization of robust strong coupling and entanglement between distant quantum emitters (QEs) is very important for scalable quantum information processes. However, it is hard to achieve it based on conventional systems. Here, we propose theoretically and demonstrate numerically a scheme to realize such strong coupling and entanglement. Our scheme is based on the photonic crystal platform with topologically protected edge state and zero-dimensional topological corner cavities. When the QEs are put into topological cavities, the strong coupling between them can be fulfilled with the assista…
The realization of robust coherent energy transfer with a long range from a donor to an acceptor has many important applications in the field of quantum optics. However, it is hard to be realized using conventional schemes. Here, we demonstrate theoretically that the robust energy transfer can be achieved using a photonic crystal platform, which includes the topologically protected edge state and zero-dimensional topological corner cavities. When the donor and the acceptor are put into a pair of separated topological cavities, respectively, the energy transfer between them can be fulfilled wit…
Measurement-based quantum computation with continuous variables in an optical setup shows the great promise towards implementation of large-scale quantum computation, where the time-domain multiplexing approach enables us to generate the large-scale cluster state used to perform measurement-based quantum computation. To make effective use of the advantage of the time-domain multiplexing approach, in this paper, we propose the method to generate the large-scale 3-dimensional cluster state which is a platform for topologically protected measurement-based quantum computation. Our method combines …
Topological quantum computation (TQC) is one of the most striking architectures that can realize fault-tolerant quantum computers. In TQC, the logical space and the quantum gates are topologically protected, i.e., robust against local disturbances. The topological protection, however, requires rather complicated lattice models and hard-to-manipulate dynamics; even the simplest system that can realize universal TQC--the Fibonacci anyon system--lacks a physical realization, let alone braiding the non-Abelian anyons. Here, we propose a disk model that can realize the Fibonacci anyon system, and c…
We propose a simple setup of Rydberg atoms in a honeycomb lattice which gives rise to topologically protected edge states. The proposal is based on the combination of dipolar exchange interaction, which couples the internal angular momentum and the orbital degree of freedom of a Rydberg excitation, and a static magnetic field breaking time reversal symmetry. We demonstrate that for realistic experimental parameters, signatures of topologically protected edge states are present in small systems with as few as 10 atoms. Our analysis paves the way for the experimental realization of Rydberg syste…
The $π$-ring qubit array is described using quasiclassical approaches that are shown to be accurate and give clarity to the complex energy landscape of connected vortex qubits. Using the techniques, large arrays of Josephson junction systems can be designed, including phase shift devices. Herein, connected arrays of loops containing $π$ junctions are described. These techniques are useful for design of quantum computers based on superconducting technologies, hybrid quantum technologies and quantum networks.
We show how to realize quantum state transfer between distant qubits using the chiral edge states of a two-dimensional topological spin system. Our implementation based on Rydberg atoms allows to realize the quantum state transfer protocol in state of the art experimental setups. In particular, we show how to adapt the standard state transfer protocol to make it robust against dispersive and disorder effects.
It is shown that quantum walks on one-dimensional arrays of special linear-optical units allow the simulation of discrete-time Hamiltonian systems with distinct topological phases. In particular, a slightly modified version of the Su-Schrieffer-Heeger (SSH) system can be simulated, which exhibits states of nonzero winding number and has topologically protected boundary states. In the large-system limit this approach uses quadratically fewer resources to carry out quantum simulations than previous linear-optical approaches and can be readily generalized to higher-dimensional systems. The basic …
We study topological phenomena of quantum walks by implementing a novel protocol that extends the range of accessible properties to the eigenvalues of the walk operator. To this end, we experimentally realise for the first time a split-step quantum walk with decoupling, which allows for investigating the effect of a bulk-boundary while realising only a single bulk configuration. We approximate the symmetry protected edge states with high similarities and read out the phase relative to a reference for all modes. In this way we observe eigenvalues which are distinguished by the presence or absen…
Measurement-based quantum computation describes a scheme where entanglement of resource states is utilized to simulate arbitrary quantum gates via local measurements. Recent works suggest that symmetry-protected topologically non-trivial, short-ranged entanged states are promising candidates for such a resource. Miller and Miyake [NPJ Quantum Information 2, 16036 (2016)] recently constructed a particular $\mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-protected topological state on the Union-Jack lattice and established its quantum computational universality. However, they sugg…
Symmetry-protected topologically ordered states for universal quantum computation
基于测量的量子计算是一种量子信息处理模型，它利用对适当纠缠的资源态的局部测量来实现量子门。对普遍资源状态的完整描述仍然缺失。在基于测量的量子计算中，一维保序拓扑可以用来保护某些量子门。本文证明了任意格点上的二维元格态在对称性分数化下具有非平凡的保序拓扑，是量子计算的通用资源态。我们关于任意二维格上的非平凡保序拓扑序的结果是基于Chen，Gu，Liu和Wen [Phys. Rev. B \textbf{87}，155114（2013）]在正方形格上的最近构造的扩展。
College of Physics and Electronic Science, Hubei Normal University（湖北师范大学物理与电子科学学院）；Hubei Engineering Institute（湖北工程学院）；State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University（山西大学量子光学与量子光学器件国家重点实验室激光光谱研究所）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
The transport of a particle in the presence of a potential that changes periodically in space and in time can be characterized by the amount of work needed to shift a particle by a single spatial period of the potential. In general, this amount of work, when averaged over a single temporal period of the potential, can take any value in a continuous fashion. Here we present a topological effect inducing the quantization of the average work. We find that this work is equal to the first Chern number calculated in a unit cell of a space-time lattice. Hence, this quantization of the average work is…
Entangled multiphoton states lie at the heart of quantum information, computing, and communications. In recent years, topology has risen as a new avenue to robustly transport quantum states in the presence of fabrication defects, disorder and other noise sources. Whereas topological protection of single photons and correlated photons has been recently demonstrated experimentally, the observation of topologically protected entangled states has thus far remained elusive. Here, we experimentally demonstrate the topological protection of spatially-entangled biphoton states. We observe robustness i…
Slow light waveguides are advantageous for implementing high-performance single-photon sources required for scalable operation of integrated quantum photonic circuits (IQPCs), though such waveguides are known to suffer from propagation loss due to backscattering. A way to overcome the drawback is to use topological photonics, in which robust waveguiding in topologically-protected optical modes has recently been demonstrated. Here, we report single-photon sources using single quantum dots (QDs) embedded in topological slow light waveguides based on valley photonic crystals. We observe Purcell-e…
What kinds of symmetry-protected topologically ordered (SPTO) ground states can be used for universal measurement-based quantum computation in a similar fashion to the 2D cluster state? 2D SPTO states are classified not only by global on-site symmetries but also by subsystem symmetries, which are fine-grained symmetries dependent on the lattice geometry. Recently, all states within so-called SPTO cluster phases on the square and hexagonal lattices have been shown to be universal, based on the presence of subsystem symmetries and associated structures of quantum cellular automata. Motivated by …
Imaging topologically protected transport with quantum degenerate gases
导电表面附近的超冷和量子简并气体可以作为电子电流流动的灵敏、高分辨率和大面积探针。先前的工作已经通过使用超冷和玻色-爱因斯坦凝聚原子与原子芯片阱保持微米的表面来成像金线中晶界周围的传输。我们表明，原子芯片显微镜可以适用于有用的目的，在材料的上下文中表现出拓扑保护的表面运输。通过光刻定制的拓扑绝缘体（TI）的表面缺陷的电流--理想化和具有典型的Bi $_{2}$ Se $_{3}$的带结构和导电性-进行了数值计算。我们建议，成像电流的流动模式，使一个理想的TI从一个有限的体积-表面电导率比的分化，具体地说，这个比例的确定可能是通过成像周围的沟槽蚀刻到TI的表面运输。
Fully frustrated Josephson junction ladders with Mobius boundary conditions as topologically protected qubits
我们展示了如何通过使用具有Mobius边界条件的完全阻挫的约瑟夫森结阶梯（JJL）来实现“受保护”的量子比特。这种系统最近已经在扭曲共形场论（CFT）方法（Mod. Phys. Lett. A 15（2000）1679; Nucl.Phys.B641（2002）547），并且显示出发展通量分级现象（Eur. J. B 49（2006）83）。在将系统的基态的拓扑性质与半通量量子的存在联系起来时，充分利用了“闭合”几何的相关性，并预测了拓扑秩序的出现（JSTAT（2005）P03006）。本文分析了基态在绝热磁通量变化下的稳定性和变换性质，并提出了实现防止退相干的固态量子比特的深刻后果。
Recently, effects of nonlinearity on topologically nontrivial systems have attracted attention and the stability of topologically protected edge states has been studied for a quantum walk with nonlinear effects, which is akin to time-periodically driven systems (Floquet systems). In the previous work, it has been found that the edge states can be stable attractors or unstable repellers depending on their intrinsic topological property, while the stability is not affected by the strength of nonlinearity. In the present work, we find additional bifurcations at which edge states change from stabl…
Quantum entanglement, as the strictly non-classical phenomena, is the kernel of quantum computing and quantum simulation, and has been widely applied ranging from fundamental tests of quantum physics to quantum information processing. The decoherence of quantum states restricts the capability of building quantum simulators and quantum computers in a scalable fashion. Meanwhile, the topological phase is found inherently capable of protecting physical fields from unavoidable fabrication-induced disorder, which inspires the potential application of topological protection on quantum states. Here, …
An edge state is a time-harmonic solution of a conservative wave system, e.g. Schroedinger, Maxwell, which is propagating (plane-wave-like) parallel to, and localized transverse to, a line-defect or "edge". Topologically protected edge states are edge states which are stable against spatially localized (even strong) deformations of the edge. First studied in the context of the quantum Hall effect, protected edge states have attracted huge interest due to their role in the field of topological insulators. Theoretical understanding of topological protection has mainly come from discrete (tight-b…
Topologically protected Bell-cat states in a simple spin model
McMaster University（麦克马斯特大学）；Perimeter Institute for Theoretical Physics（珀蒂默理论物理研究所）；The University of Oklahoma（俄克拉荷马大学）；University of Victoria（维多利亚大学）
Many-body-localized (MBL) phases can be topologically distinct, but distinguishing these phases using order parameters can be challenging. Here we show how topologically distinct local integrals of motion, variationally parametrized by quantum circuits, can be used to numerically demonstrate the topological inequivalence of MBL phases. We illustrate our approach on a fermionic chain where both topologically distinct MBL phases and benchmark comparisons to order parameters are possible. We also use our approach, augmented by the DMRG-X algorithm, to extract high-energy topological doublets. We …
