Vol.17
No.15&16,
December 1, 2017
Research Articles:
Better protocol for XOR
game using communication protocol and nonlocal boxes
(pp1261-1276)
Ryuhei
Mori
Buhrman
showed that an efficient communication protocol implies a reliable XOR
game protocol. This idea
rederives
Linial
and
Shraibman's lower bound of
randomized and quantum communication complexities, which was derived by
using factorization norms, with worse constant factor in much more
intuitive way. In this work, we improve and generalize
Buhrman's
idea, and obtain a class of lower bounds for randomized communication
complexity including an exact
Linial
and
Shraibman's lower bound as a
special case. In the proof, we explicitly construct a protocol for XOR
game from a randomized communication protocol by using a concept of
nonlocal boxes and Paw\l
owski
et~al.'s
elegant protocol, which was used for showing the violation of
information causality in
superquantum
theories.
Quantum communication
with continuum single-photon, two-photon and coherent states
(pp1277-1291)
F.
Franklin S. Rios, A. Geovan de A.H. Guerra, and R.Viana Ramos
In this work, we analyze
the behavior of continuum single-photon, two-photon and coherent states
in some quantum communication schemes. In particular, we consider the
single-photon in a Mach-Zenhder interferometer, the Hong-Ou-Mandel
interference, the quantum bit commitment protocol and a new protocol for
secure transmission of sampled analog signals. Furthermore, it is shown
an equation for estimating the spectral distribution of the
single-photon produced by a heralded single-photon source using
four-wave mixing in an optical fiber.
Generalized coherent
states, reproducing kernels, and quantum support vector machines
(pp1292-1306)
Rupak
Chatterjee and Ting Yu
The support vector
machine (SVM)
is a popular machine learning classification method which produces a
nonlinear decision boundary in a feature space by constructing linear
boundaries in a transformed Hilbert space. It is well known that these
algorithms when executed on a classical computer do not scale well with
the size of the feature space both in terms of data points and
dimensionality.
One of the most significant limitations of classical algorithms using
non-linear kernels is that the kernel function has to be evaluated for
all pairs of input feature vectors which themselves may be of
substantially high dimension. This can lead to computationally excessive
times during training and during the prediction process for a new data
point. Here, we propose using both canonical and generalized coherent
states to calculate specific nonlinear kernel functions. The key link
will be the reproducing kernel Hilbert space (RKHS)
property for
SVMs
that naturally arise from canonical and generalized coherent states.
Specifically, we discuss the evaluation of radial kernels through a
positive operator valued measure (POVM)
on a quantum optical system based on canonical coherent states. A
similar procedure may also lead to calculations of kernels not usually
used in classical algorithms such as those arising from generalized
coherent states.
Weight reduction for
quantum codes
(pp1307-1334)
Mathew
B. Hastings
We present an algorithm
that takes a
CSS
stabilizer code as input, and outputs another
CSS
stabilizer code such that the stabilizer generators all have weights
$O(1)$
and such that $O(1)$
generators act on any given
qubit.
The number of logical
qubits
is unchanged by the procedure, while we give bounds on the increase in
number of physical
qubits
and in the effect on distance and other code parameters, such as
soundness (as a locally testable code) and ``cosoundness"
(defined later). Applications are discussed, including to codes
from high-dimensional manifolds which have logarithmic weight
stabilizers. Assuming a conjecture in geometry\cite{hdm},
this allows the construction of
CSS
stabilizer codes with generator weight
$O(1)$
and almost linear distance. Another application of the
construction is to increasing the distance to
$X$
or $Z$
errors, whichever is smaller, so that the two distances are equal.
Online scheduled
execution of quantum circuits protected by surface codes
(pp1335-1348)
Alexandru
Paler, Austin G. Fowler, and Robert Wille
Quantum circuits are the
preferred formalism for expressing quantum information processing tasks.
Quantum circuit design automation methods mostly use a waterfall
approach and consider that high level circuit descriptions are hardware
agnostic. This assumption has lead to a static circuit perspective: the
number of quantum bits and quantum gates is determined before circuit
execution and everything is considered reliable with zero probability of
failure. Many different schemes for achieving reliable fault-tolerant
quantum computation exist, with different schemes suitable for different
architectures. A number of large experimental groups are developing
architectures well suited to being protected by surface quantum error
correcting codes. Such circuits could include unreliable logical
elements, such as state distillation, whose failure can be determined
only after their actual execution. Therefore, practical logical
circuits, as envisaged by many groups, are likely to have a dynamic
structure. This requires an online scheduling of their execution: one
knows for sure what needs to be executed only after previous elements
have finished executing. This work shows that scheduling shares
similarities with place and route methods. The work also introduces the
first online schedulers of quantum circuits protected by surface codes.
The work also highlights scheduling efficiency by comparing the new
methods with state of the art static scheduling of surface code
protected fault-tolerant circuits.
Quaternionic quantum
walks of Szegedy type and zeta functions of graphs
(pp1349-1371)
Norio
Konno, Kaname Matsue, Hideo Mitsuhashi and Iwao Sato
We define a
quaternionic
extension of the
Szegedy
walk on a graph and study its right spectral properties. The condition
for the transition matrix of the
quaternionic
Szegedy
walk on a graph to be
quaternionic
unitary is given. In order to derive the spectral mapping theorem for
the
quaternionic
Szegedy
walk, we derive a
quaternionic
extension of the determinant expression of the second weighted zeta
function of a graph. Our main results determine explicitly all the right
eigenvalues of the
quaternionic
Szegedy
walk by using complex right eigenvalues of the corresponding doubly
weighted matrix. We also show the way to obtain
eigenvectors
corresponding to right eigenvalues derived from those of doubly weighted
matrix.
Noise in
one-dimensional measurement-based quantum computing
(pp1372-1397)
Nairi
Usher and Dan E. Browne
Measurement-Based
Quantum Computing (MBQC)
is an alternative to the quantum circuit model, whereby the computation
proceeds via measurements on an entangled resource state. Noise
processes are a major experimental challenge to the construction of a
quantum computer. Here, we investigate how noise processes affecting
physical states affect the performed computation by considering
MBQC
on a one-dimensional cluster state. This allows us to break down the
computation in a sequence of building blocks and map physical errors to
logical errors. Next, we extend the Matrix Product State construction to
mixed states (which is known as Matrix Product Operators) and once again
map the effect of physical noise to logical noise acting within the
correlation space. This approach allows us to consider more
general errors than the conventional Pauli errors, and could be used in
order to simulate noisy quantum computation.
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