Vol.18 No.3&4, March
1, 2018
Research Articles:
Properties of quantum stochastic walks from the asymptotic scaling
exponent
(pp0181-0197)
Krzysztof Domino, Adam Glos, Mateusz Ostaszewski,
Lukasz Pawela,
and Przemyslaw Sadowski
This work focuses on the study of
quantum stochastic walks, which are a generalization of coherent,
\ie{}
unitary quantum walks. Our main goal is to present a measure of a
coherence of the walk. To this end, we utilize the asymptotic scaling
exponent of the second moment of the walk
\ie{}
of the mean squared distance covered by a walk. As the quantum
stochastic walk model encompasses both classical random walks and
quantum walks, we are interested how the continuous change from one
regime to the other influences the asymptotic scaling exponent. Moreover
this model allows for behavior which is not found in any of the
previously mentioned model -- a model with global dissipation. We derive
the probability distribution for the walker, and determine the
asymptotic scaling exponent analytically, showing that ballistic regime
of the walk is maintained even at large dissipation strength.
Adversary lower bounds for the collision and the set equality problems
(pp0198-0222)
Aleksandrs Belovs and Ansis Rosmanis
We prove tight
$\Omega(n^{1/3})$
lower bounds on the quantum query complexity of the
\cpp
and the \sep
problems, provided that the size of the alphabet is large enough. We do
this using the negative-weight adversary method. Thus, we reprove the
result by
Aaronson
and Shi,
as well as a more recent development by
Zhandry.
Constructing new
q-ary quantum MDS codes with distances bigger than q/2 from
generator matrices
(pp0223-0230)
Xianmang He
The construction of quantum
error-correcting codes has been an active field of quantum information
theory since the publication of
\cite{Shor1995Scheme,Steane1998Enlargement,Laflamme1996Perfect}.
It is becoming more and more difficult to construct some new
quantum MDS codes with large
minimum distance. In this paper, based on the approach developed in the
paper \cite{NewHeMDS2016},
we construct several new classes of quantum MDS codes. The quantum MDS
codes exhibited here have not been constructed before and the distance
parameters are bigger than $\frac{q}{2}$.
Quantum information transmission through a qubit chain with quasi-local
dissipation
(pp0231-0246)
Roya Radgohar, Laleh Memarzadeh, and Stefano Mancini
We study quantum information
transmission in a Heisenberg-XY chain where
qubits
are affected by quasi-local environment action and compare it with the
case of local action of the environment. We find that for open boundary
conditions the former situation always improves quantum state transfer
process, especially for short chains. In contrast, for closed boundary
conditions quasi-local environment results advantageous in the strong
noise regime. When the noise strength is comparable with the XY
interaction strength, the state transfer fidelity through chain of
odd/even number of
qubits
in presence of quasi-local environment results smaller/greater than that
in presence of local environment.
Rapid
and robust generation of Einstein-–Podolsky–-Rosen pairs with spin
chains
(pp0247-0264)
Kieran N. Wilkinson, Marta P. Estarellas, Timothy P.
Spiller, and Irene D'Amico
We investigate the ability of
dimerized
spin chains with defects to generate
EPR
pairs to very high fidelity through their natural dynamics. We propose
two protocols based on different
initializations of the system,
which yield the same maximally entangled Bell state after a
characteristic time. This entangling time can be varied through
engineering the weak/strong couplings' ratio of the chain, with larger
values giving rise to an exponentially faster quantum entangling
operation. We demonstrate that there is a set of characteristic values
of the coupling, for which the entanglement generated remains extremely
high. We investigate the robustness of both protocols to diagonal and
off-diagonal disorder. Our results demonstrate extremely strong
robustness to both perturbation types, up to strength of 50\%
of the weak coupling. Robustness to disorder can be further enhanced by
increasing the coupling ratio. The combination of these properties makes
the use of our proposed device suitable for the rapid and robust
generation of Bell states in quantum information processing
applications.
Multi-qubit non-Markovian dynamics in
photonic crystal with
infinite cavity-array structure
(pp0265-0282)
Heng-Na Xiong, Yi Li, Yixiao Huang, and Zichun Le
We study the exact non-Markovian
dynamics of a multi-qubit system coupled to a photonic-crystal waveguide
with infinite cavity-array structure. A general solution of the
evolution state of the system is solved for a general initial state in
the single-excitation subspace. With this solution, we find that the
non-Markovian effect of the environment on the system could be enhanced
not only by increasing the system-environment coupling strength but also
by adding the qubit number in the system. The explicit non-Markovian
dynamics are discussed under two initial states to see the non-Markovian
effect on entanglement preservation and entanglement generation. We find
that the non-Markovian effect tends to preserve the system in its
initial state.
Space-efficient classical and quantum algorithms for the shortest
vector problem
(pp0283-0305)
Yanlin Chen, Kai-Min Chung, and Ching-Yi Lai
A lattice is the integer span of some
linearly independent vectors. Lattice problems have many significant
applications in coding theory and cryptographic systems for their
conjectured hardness. The Shortest Vector Problem (SVP), which asks to
find a shortest nonzero vector in a lattice, is one of the well-known
problems that are believed to be hard to solve, even with a quantum
computer. In this paper we propose space-efficient
classical and quantum algorithms for solving SVP. Currently
the best time-efficient algorithm for solving SVP
takes $2^{n+o(n)}$
time and $2^{n+o(n)}$
space. Our classical algorithm takes
$2^{2.05n+o(n)}$
time to solve SVP
and it requires only
$2^{0.5n+o(n)}$ space. We then
adapt our classical algorithm to a quantum version, which can solve
SVP
in time $2^{1.2553n+o(n)}$
with $2^{0.5n+o(n)}$
classical space and only poly$(n)$
qubits.
Hyperbolic quantum color
codes
(pp0306-0318)
Waldir Silva Soares Jr. and Eduardo Brandani da Silva
Current work presents a new approach
to quantum color codes on compact surfaces with genus
$g \geq 2$
using the identification of these surfaces with hyperbolic polygons and
hyperbolic tessellations. We show that this method may give rise to
color codes with a very good parameters and we present tables with
several examples of these codes whose parameters had not been shown
before. We also present a family of codes with minimum distance
$d=4$
and the encoding rate asymptotically going to 1 while
$n \rightarrow \infty$.
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