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The color code is both an interesting example of an exactly solved

topologically ordered phase of matter and also among the most promising

candidate models to realize fault-tolerant quantum computation with minimal

resource overhead. The contributions of this work are threefold. First of all,

we build upon the abstract theory of boundaries and domain walls of topological

phases of matter to comprehensively catalog the objects realizable in color

codes. Together with our classification we also provide lattice representations

The creation of delocalized coherent superpositions of quantum systems

experiencing different relativistic effects is an important milestone in future

research at the interface of gravity and quantum mechanics. This could be

achieved by generating a superposition of quantum clocks that follow paths with

different gravitational time dilation and investigating the consequences on the

interference signal when they are eventually recombined. Light-pulse atom

Many open quantum systems encountered in both natural and synthetic

situations are embedded in classical-like baths. Often, the bath degrees of

freedom may be represented in terms of canonically conjugate coordinates, but

in some cases they may require a non-canonical or non-Hamiltonian

representation. Herein, we review an approach to the dynamics and statistical

mechanics of quantum subsystems embedded in either non-canonical or

non-Hamiltonian classical-like baths which is based on operator-valued

The permutational invariance of identical two-level systems allows for an

exponential reduction in the computational resources required to study the

Lindblad dynamics of coupled spin-boson ensembles evolving under the effect of

both local and collective noise. Here we take advantage of this speedup to

study several important physical phenomena in the presence of local incoherent

processes, in which each degree of freedom couples to its own reservoir.

Assessing the robustness of collective effects against local dissipation is

The classical and quantum mechanical correspondence for constant mass

settings is used, along with some point canonical transformation, to find the

position-dependent mass (PDM) classical and quantum Hamiltonians. The

comparison between the resulting quantum PDM-Hamiltonian and the von Roos

PDM-Hamiltonian implied that the ordering ambiguity parameters of von Roos are

strictly determined. Eliminating, in effect, the ordering ambiguity associated

with the von Roos PDM-Hamiltonian. This, consequently, played a vital role in

In a Quantum Walk (QW) the "walker" follows all possible paths at once

through the principle of quantum superposition, differentiating itself from

classical random walks where one random path is taken at a time. This

facilitates the searching of problem solution spaces faster than with classical

random walks, and holds promise for advances in dynamical quantum simulation,

biological process modelling and quantum computation. Current efforts to

implement QWs have been hindered by the complexity of handling single photons

Vertex amplitudes are elementary contributions to the transition amplitudes

in the spin foam models of quantum gravity. The purpose of this article is make

the first step towards computing vertex amplitudes with the use of quantum

algorithms. In our studies we are focused on a vertex amplitude of 3+1 D

gravity, associated with a pentagram spin-network. Furthermore, all spin labels

of the spin network are assumed to be equal $j=1/2$, which is crucial for the

Weak values have been shown to be helpful especially when considering them as

the outcomes of weak measurements. In this paper we show that in principle, the

real and imaginary parts of the weak value of any operator may be elucidated

from expectation values of suitably defined density, flux and hermitian

commutator operators. Expectation values are the outcomes of strong

(projective) measurements implying that weak values are general properties of

operators in association with pre- and post-selection and they need not be

We describe the design and implementation of a stable high-power 1064 nm

laser system to generate optical lattices for experiments with ultracold

quantum gases. The system is based on a low-noise laser amplified by an array

of four heavily modified, high-power fiber amplifiers. The beam intensity is

stabilized and controlled with a nonlinear feedback loop. Using real-time

monitoring of the resulting optical lattice, we find the stability of the

lattice site positions to be well below the lattice spacing for several hours.

In a recent publication in Nature Communications by Frauchiger and Renner

(Nat. Commun. 9, 3711 (2018)), a Gedankenexperiment was proposed, which was

claimed to be able to lead to inconsistent conclusions with a self-referential

use of quantum theory. Thus it seems to prove that quantum theory cannot

consistently describe the use of itself. Shortly after, Chen and Zhang

suggested an improvement (arXiv:1810.01080) which can made the explanation of