Topological phases protected by symmetry can occur in gapped
and---surprisingly---in critical systems. We consider non-interacting fermions
in one dimension with spinless time-reversal symmetry. It is known that the
phases are classified by a topological invariant $\omega$ and a central charge
$c$. We investigate the correlations of string operators, giving insight into
the interplay between topology and criticality. In the gapped phases, these
non-local string order parameters allow us to extract $\omega$. Remarkably,

Coherence is a basic phenomenon in quantum mechanics and considered to be an
essential resource in quantum information processing. Although the
quantification of coherence has attracted a lot of interest, the lack of
efficient methods to measure the coherence in experiments limits the
applications. We address this problem by introducing an experiment-friendly
method for coherence and spectrum estimation. This method is based on the
theory of majorization and can not only be used to prove the presence of

The entanglement and resonance energy transfer between two-level quantum
emitters are typically limited to sub-wavelength distances due to the
inherently short-range nature of the dipole-dipole interactions. Moreover, the
entanglement of quantum systems is hard to preserve for a long time period due
to decoherence and dephasing mainly caused by radiative and nonradiative
losses. In this work, we outperform the aforementioned limitations by
presenting efficient long-range inter-emitter entanglement and large

Emission and absorption of light lie at the heart of light-matter
interaction. Although the emission and absorption rates are regarded as
intrinsic properties of atoms and molecules, various ways to modify these rates
have been sought in critical applications such as quantum information
processing, metrology and light-energy harvesting. One of the promising
approaches is to utilize collective behavior of emitters as in superradiance.
Although superradiance has been observed in diverse systems, its conceptual

Experimental implementation of a quantum computing algorithm strongly relies
on the ability to construct required unitary transformations applied to the
input quantum states. In particular, near-term linear optical computing
requires universal programmable interferometers, capable of implementing an
arbitrary transformation of input optical modes. So far these devices were
composed as a circuit with well defined building blocks, such as balanced
beamsplitters. This approach is vulnerable to manufacturing imperfections

The difficulty of simulating quantum dynamics depends on the norm of the
Hamiltonian. When the Hamiltonian varies with time, the simulation complexity
should only depend on this quantity instantaneously. We develop quantum
simulation algorithms that exploit this intuition. For the case of sparse
Hamiltonian simulation, the gate complexity scales with the $L^1$ norm
$\int_{0}^{t}\mathrm{d}\tau\left\lVert H(\tau)\right\lVert_{\max}$, whereas the
best previous results scale with $t\max_{\tau\in[0,t]}\left\lVert

We show that the cylindrical symmetry of the eigenvectors of the photon
position operator with commuting components, x, reflects the E(2) symmetry of
the photon little group. The eigenvectors of x form a basis of localized states
that have definite angular momentum, J, parallel to their common axis of
symmetry. This basis is well suited to the description of "twisted light" that
has been the subject of many recent experiments and calculations. Rotation of
the axis of symmetry of this basis results in the observed Berry phase

We study quantum anomaly detection with density estimation and multivariate
Gaussian distribution. Both algorithms are constructed using the standard
gate-based model of quantum computing. Compared with the corresponding
classical algorithms, the resource complexities of our quantum algorithm are
logarithmic in the dimensionality of quantum states and the number of training
quantum states. We also present a quantum procedure for efficiently estimating
the determinant of any Hermitian operators $\mathcal{A}\in\mathcal{R}^{N\times

Weyl points, synthetic magnetic monopoles in the 3D momentum space, are the
key features of topological Weyl semimetals. The observation of Weyl points in
ultracold atomic gases usually relies on the realization of high-dimensional
spin-orbit coupling (SOC) for two pseudospin states (% \textit{i.e.,}
spin-1/2), which requires complex laser configurations and precise control of
laser parameters, thus has not been realized in experiment. Here we propose
that robust Wely points can be realized using 1D triple-well superlattices