# All

We revisit the issue of defining the entropy of a spatial region in a broad

class of quantum theories. In theories with explicit regularizations, working

within an elementary but general algebraic framework applicable to matter and

gauge theories alike, we give precise path integral expressions for three known

types of entanglement entropy that we call full, distillable, and

gauge-invariant. For a class of gauge theories that do not necessarily have a

regularization in our framework, including Chern-Simons theory, we describe a

For the characterization of dynamics in quantum many-body systems the

question how information spreads and becomes distributed over the constituent

degrees of freedom is of fundamental interest. The delocalization of

information under many-body dynamics has been dubbed "scrambling" and

out-of-time-order correlators were proposed to probe this behavior. In this

work we investigate the time-evolution of tripartite information as a natural

operator-independent measure of scrambling, which quantifies to which extent

We study scattering of propagating microwave fields by a DC-voltage biased

Josephson junction. At sub-gap voltages, a small Josephson junction works

merely as a non-linear boundary that can absorb, amplify, and diversely convert

propagating microwaves. In the leading-order perturbation theory of the

Josephson coupling energy, the spectral density and quadrature fluctuations of

scattered thermal and coherent radiation can be described in terms of the

well-known $P(E)$ function. Applying this, we study how thermal and coherent

The Noisy Intermediate-Scale Quantum (NISQ) technology is currently

investigated by major players in the field to build the first practically

useful quantum computer. IBM QX architectures are the first ones which are

already publicly available today. However, in order to use them, the respective

quantum circuits have to be compiled for the respectively used target

architecture. While first approaches have been proposed for this purpose, they

are infeasible for a certain set of SU(4) quantum circuits which recently have

The resonance fluorescence of a four-level atom in J = 1/2 to J = 1/2

transition driven by two coherent fields is studied. We find that the

incoherent fluorescence spectrum shows a direct indication of vacuum-induced

coherence in the atomic system. We show that such coherence manifests itself

via an enhancement or suppression of the spectral peaks in the $\pi$-polarized

fluorescence. The effect of the relative phase of the driving fields on the

spectral features is also investigated. We show that phase-dependent

Optimization problems in disciplines such as machine learning are commonly

solved with iterative methods. Gradient descent algorithms find local minima by

moving along the direction of steepest descent while Newton's method takes into

account curvature information and thereby often improves convergence. Here, we

develop quantum versions of these iterative optimization algorithms and apply

them to polynomial optimization with a unit norm constraint. In each step,

We introduce a protocol capable of generating a general measurement operator

for a mechanical resonator. The technique requires a qubit-resonator

interaction and uses a coherent pulse to drive qubit transitions. This is

followed by projective measurement of the qubit's energy, constraining the

resonator in a state that depends on the pulse shape. The freedom to choose a

pulse shape for the coherent drive enables an arbitrary position-basis

measurement operator. Using this measurement operator, we outline a two pulse

Quantum computers, which take advantage of the superposition and entanglement

of physical states, could outperform their classical counterparts in solving

problems with technological impact, such as factoring large numbers and

searching databases. A quantum processor executes algorithms by applying a

programmable sequence of gates to an initialized state of qubits, which

coherently evolves into a final state containing the result of the computation.

Although quantum processors with a few qubits have been demonstrated on

We propose the concept of machine learning configuration interaction (MLCI)

whereby an artificial neural network is trained on-the-fly to predict important

new configurations in an iterative selected configuration interaction

procedure. We demonstrate that the neural network can discriminate between

important and unimportant configurations, that it has not been trained on, much

better than by chance. MLCI is then used to find compact wavefunctions for

carbon monoxide at both stretched and equilibrium geometries. We also consider

Valid transformations between quantum states are necessarily described by

completely positive maps, instead of just positive maps. Positive but not

completely positive maps such as the transposition map cannot be implemented

due to the existence of entanglement in composite quantum systems, but there

are classes of states for which the positivity is guaranteed, e.g., states not

correlated to other systems. In this paper, we introduce the concept of N-copy