# All

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

We consider an algorithm to approximate complex-valued periodic functions

$f(e^{i\theta})$ as a matrix element of a product of $SU(2)$-valued functions,

which underlies so-called quantum signal processing. We prove that the

algorithm runs in time $\mathcal O(N^3 \mathrm{polylog}(N/\epsilon))$ under the

random-access memory model of computation where $N$ is the degree of the

polynomial that approximates $f$ with accuracy $\epsilon$; previous efficiency

claim assumed a strong arithmetic model of computation and lacked numerical

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

We construct efficient deterministic dynamical decoupling schemes protecting

continuous variable degrees of freedom. Our schemes target decoherence induced

by quadratic system-bath interactions with analytic time-dependence. We show

how to suppress such interactions to $N$-th order using only $N$~pulses.

Furthermore, we show to homogenize a $2^m$-mode bosonic system using only

$(N+1)^{2m+1}$ pulses, yielding - up to $N$-th order - an effective evolution

We report on numerical calculations of the spontaneous emission rate of a

Rydberg-excited sodium atom in the vicinity of an optical nanofibre. In

particular, we study how this rate varies with the distance of the atom to the

fibre, the fibre's radius, the symmetry s or p of the Rydberg state as well as

its principal quantum number. We find that a fraction of the spontaneously

emitted light can be captured and guided along the fibre. This suggests that

such a setup could be used for networking atomic ensembles, manipulated in a

We investigate the time-optimal solution of the selective control of two

uncoupled spin 1/2 particles. Using the Pontryagin Maximum Principle, we derive

the global time-optimal pulses for two spins with different offsets. We show

that the Pontryagin Hamiltonian can be written as a one-dimensional effective

Hamiltonian. The optimal fields can be expressed analytically in terms of

elliptic integrals. The time-optimal control problem is solved for the

selective inversion and excitation processes. A bifurcation in the structure of

Choosing the right first quantization basis in quantum optics is critical for

the interpretation of experimental results. The usual frequency basis is, for

instance, inappropriate for short, subcycle waveforms. We derive first

quantization in time domain, and apply the results to ultrashort pulses

propagating along unidimensional waveguides. We show how to compute the

statistics of the photon counts, or that of their times of arrival. We also

extend the concept of quadratures to the time domain, making use of the Hilbert

Exploiting a well-established mapping from a d-dimensional quantum

Hamiltonian to a d+1-dimensional classical Hamiltonian that is commonly used in

software quantum Monte Carlo algorithms, we propose a scalable hardware

emulator where quantum circuits are emulated with room temperature p-bits. The

proposed emulator operates with probabilistic bits (p-bit) that fluctuate

between logic 0 and 1, that are suitably interconnected with a crossbar of

resistors or conventional CMOS devices. One particularly compact hardware

Given a general $d$-dimensional unitary operation $U_d$ for which, apart from

the dimension, its description is unknown, is it possible to implement its

inverse operation $U_d^{-1}$ with a universal protocol that works for every

unitary $U_d$? How does the situation change when $k$ uses of unitary operation

$U_d$ are allowed? In this paper we show that any universal protocol

implementing the inverse of a general unitary $U_d$ with a positive heralded

probability requires at least $d-1$ uses of $U_d$. For the cases where $k\geq

Trapped-ion quantum information processors offer many advantages for

achieving high-fidelity operations on a large number of qubits, but current

experiments require bulky external equipment for classical and quantum control

of many ions. We demonstrate the cryogenic operation of an ion-trap that

incorporates monolithically-integrated high-voltage CMOS electronics ($\pm

8\mathrm{V}$ full swing) to generate surface-electrode control potentials

without the need for external, analog voltage sources. A serial bus programs an