We study the quantum fidelity (groundstate overlap) near quantum phase transitions of the Ising universality class in one dimensional (1D) systems of finite size L. Prominent examples occur in magnetic systems (e.g. spin-Peierls, the anisotropic XY model), and in 1D topological insulators of any topologically nontrivial Altland-Zirnbauer-Kitaev universality class. The rescaled fidelity susceptibility is a function of the only dimensionless parameter LM, where 2M is the gap in the fermionic spectrum. We present analytic expressions for the fidelity susceptibility for periodic and open boundaries conditions with zero, one or two edgestates. The latter are shown to have a crucial impact and alter the susceptibility both quantitatively and qualitatively. We support our analytical solutions with numerical data.
Robust high-fidelity universal set of quantum gates through non-adiabatic rapid passage
我们展示了如何使用单一形式的非绝热快速通道来实现一个强大的高保真通用量子门集，其参数被优化以最大化门保真度和奖励门鲁棒性。通用集合中的每个门都以0.99988 < F < 0.99999范围内的保真度F工作，并且需要不超过14位（1/10，000）精度的控制参数。这样的精度是在商业上可用的任意波形发生器的范围内，因此，对这种高保真通用量子控制方法的实验研究似乎是可行的。
Fast and high-fidelity transfer of edge states via dynamical control of topological phases and effects of dissipation
Hokkaido University（北海道大学）；National Institute of Technology, Asahikawa College（国立长春冈技术短期大学）；RIKEN（理化学研究所）；Ritsumeikan University（立命馆大学）；Osaka University（大阪大学）；The University of Tokyo（东京大学）
Ultrafast helicity control of surface currents in topological insulators with near-unity fidelity
近年来，出现了一类称为三维拓扑绝缘体的固态材料。在本体中，拓扑绝缘体的行为与带隙的普通绝缘体一样。在表面，存在导电的无带隙状态，显示出显著的性质，如螺旋狄拉克色散和抑制自旋极化的载流子的背散射。通过传输实验表征和控制表面状态往往受到阻碍，但在低温下的剩余散装贡献。在这里，我们表明，在Bi 2 Se 3的表面电流可以控制圆偏振光在皮秒的时间尺度上的保真度接近统一，即使在室温下。我们揭示了这种超快的螺旋度依赖的表面电流的时间分离的光致热电和漂移电流的散装。我们的研究结果揭示了基于拓扑绝缘体表面电流的超快光电子器件的功能。
We investigate the Loschmidt amplitude and dynamical quantum phase transitions in multiband one dimensional topological insulators. For this purpose we introduce a new solvable multiband model based on the Su-Schrieffer-Heeger model, generalized to unit cells containing many atoms but with the same symmetry properties. Such models have a richer structure of dynamical quantum phase transitions than the simple two-band topological insulator models typically considered previously, with both quasiperiodic and aperiodic dynamical quantum phase transitions present. Moreover the aperiodic transitions…
The Uhlmann connection is a mixed state generalisation of the Berry connection. The latter has a very important role in the study of topological phases at zero temperature. Closely related, the quantum fidelity is an information theoretical quantity which is a measure of distinguishability of quantum states. Moreover, it has been extensively used in the analysis of quantum phase transitions. In this work, we study topological phase transitions in 1D and 2D topological superconductors with long-range hopping and pairing amplitudes, using the fidelity and the quantity $Δ$ closely related to the …
We propose the generation of entangled qubits by utilizing the properties of edge states appearing at one end of a periodically driven (Floquet) superconducting qubit chain. Such qubits are naturally protected by the system's topology and their manipulation is possible through adiabatic control of the system parameters. By utilizing a Y-junction geometry, we then develop a protocol to perform high-fidelity transfer of entangled qubits from one end to another end of a qubit chain. Our quantum state transfer protocol is found to be robust against disorder and imperfection in the system parameter…
We study topological properties of one-dimensional non-Hermitian systems without chiral symmetry and give phase diagrams characterized by topological invariants $ν_E$ and $ν_{total}$, associated with complex energy vorticity and summation of Berry phases of complex bands, respectively. In the absence of chiral symmetry, we find that the phase diagram determined by $ν_E$ is different from $ν_{tot}$. While the transition between phases with different $ν_{E}$ is closely related to the band-touching point, the transition between different $ν_{tot}$ is irrelevant to the band-touching condition. We …
Fault-tolerant quantum computers which can solve hard problems rely on quantum error correction. One of the most promising error correction codes is the surface code, which requires universal gate fidelities exceeding the error correction threshold of 99 per cent. Among many qubit platforms, only superconducting circuits, trapped ions, and nitrogen-vacancy centers in diamond have delivered those requirements. Electron spin qubits in silicon are particularly promising for a large-scale quantum computer due to their nanofabrication capability, but the two-qubit gate fidelity has been limited to …
We elaborate that for topological insulators and topological superconductors described by Dirac models in any dimension and symmetry class, the topological order can be mapped to lattice sites by a universal topological marker. Deriving from a recently discovered momentum-space universal topological invariant, we introduce a topological operator that consists of alternating projectors to filled and empty lattice eigenstates and the position operators, multiplied by the Dirac matrices that are omitted in the Hamiltonian. The topological operator projected to lattice sites yields the topological…
We examine the magnetic susceptibility of topological insulators microscopically and find that the orbital-Zeeman (OZ) cross term, the cross term between the orbital effect and the spin Zeeman effect, is directly related to the Berry curvature when the $z$-component of spin is conserved. In particular, the OZ cross term reflects the spin Chern number, which results in the quantization of the magnetic susceptibility jump at the topological phase transition. The magnitude of the jump is in units of the universal value $4|e|μ_{\rm B}/h$. The physical origin of this quantization is clarified. We a…
Topological phases of the famous Altland-Zirnbauer (AZ) tenfold classes are defined on the equilibrium ground states. Whether such equilibrium topological phases have universal correspondence to far-from-equilibrium quantum dynamics is a fundamental issue of both theoretical and experimental importance. Here we uncover the universal topological quench dynamics linking to the equilibrium topological phases for the complete AZ tenfold classes, with a general framework being established. We show a fundamental result that a $d$-dimensional topological phase of the tenfold class, with an integer in…
Indications of the topological transport by the universal conductance fluctuations in the Bi2Te2Se microflakes
通用电导波动（UCFs）提取在体绝缘Bi 2 Te 2Se微片的磁阻响应。它的二维特性证明了由场倾斜磁阻测量。其来源于表面电子，这是由于在施加面内场以抑制体电子相干性的同时，UCF振幅保持不变。在考虑了一批微米级样品的系综平均后，得到了超过0.37 e2/h的本征UCF幅度。这与拓扑表面态的理论预测相一致。所有的证据都指向拓扑表面态的UCF的成功观测。
Universal driving protocol for symmetry-protected Floquet topological phasesWe propose a universal driving protocol for the realization of symmetry-protected topological phases in $2+1$ dimensional Floquet systems. Our proposal is based on the theoretical analysis of the possible symmetries of a square lattice model with pairwise nearest-neighbor coupling terms. Among the eight possible symmetry operators we identify the two relevant choices for topological phases with either time-reversal, chiral, or particle-hole symmetry. From the corresponding symmetry conditions on the protocol parameters…
We study the dynamics and readout of topological qubits encoded by zero-energy Majorana bound states in a topological superconductor. We take into account bosonic modes due to the electromagnetic environment which couple the Majorana manifold to above-gap continuum quasi-particles. This coupling causes the degenerate ground state of the topological superconductor to be dressed in a polaron-like manner by quasi-particle states and bosons, and the system to become gapless. Topological protection and hence full coherence is only maintained if the qubit is operated and read out within the low-ener…
Topological properties of materials, as manifested in the intriguing phenomena of quantum Hall effect and topological insulators, have attracted overwhelming transdisciplinary interest in recent years. Topological edge states, for instance, have been realized in versatile systems including electromagnetic-waves. Typically, topological properties are revealed in momentum space, using concepts such as Chern number and Berry phase. Here, we demonstrate a universal mapping of the topology of Dirac-like cones from momentum space to real space. We evince the mapping by exciting the cones in photonic…
Topological edge zero modes and states of self stress have been intensively studied in discrete lattices at the Maxwell point, offering robust properties concerning surface and interface stiffness and stress focusing. In this paper we present a continuum topological elasticity theory and generalize the Maxwell-Calladine index theorem to continuous elastic media. This theory not only serves as a macroscopic description for topological Maxwell lattices, but also generalizes this physics to continuous media. We define a \emph{gauge-invariant} bulk topological index, independent of microscopic det…
Disorder-enhanced topological protection and universal quantum criticality in a spin-3/2 topological superconductor
Texas Center for Superconductivity and Department of Physics, University of Houston（休斯顿大学物理系超导电性中心）；Department of Physics and Astronomy, Rice University（莱斯大学物理与天文学系）；Rice Center for Quantum Materials, Rice University（莱斯大学量子材料中心）
