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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