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

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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

- Read more about Validating and certifying stabilizer states
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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.

- Read more about Twisted Laplace maps
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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## [http://ej.iop.org/images/1751-8121/52/22/225202/aab0d98ieqn001.gif] Lie algebra. An

explicit h -spherical harmonics basis is given in terms of Jacobi polynomials.