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

# All

Quantum networking based on optical Gaussian states, although promising in

terms of scalability, is hindered by the fact that their entanglement cannot be

distilled via Gaussian operations. We show that optomechanics, integrable

(on-chip) availability, and particularly the scope to measure the mechanical

degree of freedom, can address this problem. Here, one of the optical modes of

a two-mode squeezed vacuum is injected into a single-sided Fabry-P\'{e}rot

cavity and non-linearly coupled to a mechanical oscillator. Afterward, the

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

The Schmidt-decomposition formalism is proposed to be used for evaluation of

the degree of quadrature entanglement in two-mode multiphoton states.

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

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 probe electric-field noise in a surface ion trap for ion-surface distances

$d$ between 50 and 300 $\mu\mathrm{m}$ in the normal and planar directions. We

find the noise distance dependence to scale as $d^{-2.6}$ in our trap and a

frequency dependence which is consistent with $1/f$ noise. Simulations of the

electric-field noise specific to our trap geometry provide evidence that we are

not limited by technical noise sources. Our distance scaling data is consistent