# All

We propose and analyze a scanning microscope to monitor `live' the quantum

dynamics of cold atoms in a Cavity QED setup. The microscope measures the

atomic density with subwavelength resolution via dispersive couplings to a

cavity and homodyne detection within the framework of continuous measurement

theory. We analyze two modes of operation. First, for a fixed focal point the

microscope records the wave packet dynamics of atoms with time resolution set

by the cavity lifetime. Second, a spatial scan of the microscope acts to map

We consider superconducting circuits for the purpose of simulating the

spin-boson model. The spin-boson model consists of a single two-level system

coupled to bosonic modes. In most cases, the model is considered in a limit

where the bosonic modes are sufficiently dense to form a continuous spectral

bath. A very well known case is the ohmic bath, where the density of states

grows linearly with the frequency. In the limit of weak coupling or large

temperature, this problem can be solved numerically. If the coupling is strong,

The quantum assembly language (QASM) is a popular intermediate representation

used in many quantum compilation and simulation tools to describe quantum

circuits. Currently, multiple different dialects of QASM are used in different

quantum computing tools. This makes the interaction between those tools tedious

and time-consuming due to the need for translators between theses different

syntaxes. Beside requiring a multitude of translators, the translation process

Quantum measurements based on mutually unbiased bases are commonly used in

quantum information processing, as they are generally viewed as being maximally

incompatible and complementary. Here we quantify precisely the degree of

incompatibility of mutually unbiased bases (MUB) using the notion of noise

robustness. Specifically, for sets of $k$ MUB in dimension $d$, we provide

upper and lower bounds on this quantity. Notably, we get a tight bound in

several cases, in particular for complete sets of $k=d+1$ MUB (given $d$ is a

We develop a scheme of fast forward of adiabatic spin dynamics of quantum

entangled states. We settle the quasi-adiabatic dynamics by adding the

regularization terms to the original Hamiltonian and then accelerate it with

use of a large time-scaling factor. Assuming the experimentally-realizable

candidate Hamiltonian consisting of the exchange interactions and magnetic

field, we solved the regularization terms. These terms multiplied by the

velocity function give rise to the state-dependent counter-diabatic terms. The

The investigation of macroscopic quantum phenomena is a current active area

of research that offers significant promise to advance the forefronts of both

fundamental and applied quantum science. Utilizing the exquisite precision and

control of quantum optics provides a powerful toolset for generating such

quantum states where the types and 'size' of the states that can be generated

are set by the resourcefulness of the protocol applied. In this work we present

We study the dynamics of a quantum system whose interaction with an

environment is described by a non-Markovian collision model. We identify the

relevant system-environment correlations that lead to a non-Markovian

evolution. Through an equivalent picture of the open dynamics, we introduce the

notion of "memory depth" where these correlations are established between the

system and a suitably sized memory rendering the overall system+memory

evolution Markovian. We extend our analysis to show that while most

Given a parameterized quantum circuit such that a certain setting of these

real-valued parameters corresponds to Grover's celebrated search algorithm, can

a variational algorithm recover these settings and hence learn Grover's

algorithm? We tried several constrained variations of this problem and answered

this question in the affirmative, with some caveats. Grover's quantum search

algorithm is optimal up to a constant. The success probability of Grover's

A non-Hermitian extension of the Chern insulator and its bulk-boundary

correspondence are investigated. It is shown that in addition to the robust

chiral edge states that reflect the nontrivial topology of the bulk (nonzero

Chern number), the anomalous helical edge states localized only at one edge can

appear, which are unique to the non-Hermitian Chern insulator.

A weak measurement performed on a pre- and post-selected quantum system can

result in an average value that lies outside of the observable's spectrum. This

effect, usually referred to as an "anomalous weak value", is generally believed

to be possible only when a non-trivial post-selection is performed, i.e., when

only a particular subset of the data is considered. Here we show, however, that

this is not the case in general: in scenarios in which several weak

measurements are sequentially performed, an anomalous weak value can be