Quantum cellular automata consist in arrays of identical finite-dimensional
quantum systems, evolving in discrete-time steps by iterating a unitary
operator G. Moreover the global evolution G is required to be causal (it
propagates information at a bounded speed) and translation-invariant (it acts
everywhere the same). Quantum cellular automata provide a model/architecture
for distributed quantum computation. More generally, they encompass most of
discrete-space discrete-time quantum theory. We give an overview of their

We consider classical and quantum algorithms which have a duality property:
roughly, either the algorithm provides some nontrivial improvement over random
or there exist many solutions which are significantly worse than random. This
enables one to give guarantees that the algorithm will find such a nontrivial
improvement: if few solutions exist which are much worse than random, then a
nontrivial improvement is guaranteed. The quantum algorithm is based on a

The preparation of initial superposition states of discrete-time quantum
walks (DTQWs) are necessary for the study and applications of DTQWs. In linear
optics, it is easy to prepare initial superposition states of the coin, which
are always encoded by polarization states; while the preparation of
superposition states of the walker is challenging. Based on a novel encoding
method, we here propose a DTQW protocol in linear optics which enables the
preparation of arbitrary initial superposition states of the walker and the

We demonstrate the possibility of drastically reducing the velocity of
phonons in quasi one-dimensional Bose-Einstein condensates. Our scheme consists
of a dilute dark-soliton "gas" that provide the trapping for the impurities
that surround the condensate. We tune the interaction between the impurities
and the condensate particles in such a way that the dark solitons result in an
array of {\it qutrits} (three-level structures). We compute the phonon-soliton

Quantum decoherence arises due to uncontrollable entanglement between a
system with its environment. However the effects of decoherence are often
thought of and modeled through a simpler picture in which the role of the
environment is to introduce classical noise in the system's degrees of freedom.
Here we establish necessary conditions that the classical noise models need to
satisfy to quantitatively model the decoherence. Specifically, for
pure-dephasing processes we identify well-defined statistical properties for

Author(s): Sheng-li Ma, Xin-ke Li, Xin-yu Liu, Ji-kun Xie, and Fu-li Li
We propose a quantum reservoir engineering approach for stabilizing Bell states of two superconducting qubits. The system under consideration consists of two linearly coupled superconducting transmission line resonators and two separated flux qubits, one of which is interacted with one resonator. Ap...
[Phys. Rev. A 99, 042336] Published Tue Apr 30, 2019

Author(s): Amir Kalev, Anastasios Kyrillidis, and Norbert M. Linke
We propose a measurement scheme that validates the preparation of an $n$-qubit stabilizer state. The scheme involves a measurement of $n$ Pauli observables, a priori determined from the stabilizer state and which can be realized using single-qubit gates. Based on the proposed validation scheme, we d...
[Phys. Rev. A 99, 042337] Published Tue Apr 30, 2019

We investigate the first-passage problem where a diffusive searcher stochastically resets to a fixed
position at a constant rate in a bounded domain. We put forward an analytical framework for this
problem where the resetting rate r , the resetting position x r , the initial position x 0 , the
domain size L , and the particle’s diffusion constant D are independent variables. From this we
obtain analytical expressions for the mean-first passage time, survival probability and the

We consider general Darboux maps arising from intertwining relations on second order, linear partial
differential operators, as deformations of the classical, Laplace case. We present Lax pairs for the
corresponding relations on invariants and discuss the conditions for a lattice structure analogous
to 2D Toda theory.

The Dunkl–Coulomb system in three-dimensions is introduced. The energy spectrum and the wave
functions of the system are solved by means of spectrum generating algebra techniques based on the
##IMG## [] Lie algebra. An
explicit h -spherical harmonics basis is given in terms of Jacobi polynomials.