691 research outputs found
On Protected Realizations of Quantum Information
There are two complementary approaches to realizing quantum information so
that it is protected from a given set of error operators. Both involve encoding
information by means of subsystems. One is initialization-based error
protection, which involves a quantum operation that is applied before error
events occur. The other is operator quantum error correction, which uses a
recovery operation applied after the errors. Together, the two approaches make
it clear how quantum information can be stored at all stages of a process
involving alternating error and quantum operations. In particular, there is
always a subsystem that faithfully represents the desired quantum information.
We give a definition of faithful realization of quantum information and show
that it always involves subsystems. This justifies the "subsystems principle"
for realizing quantum information. In the presence of errors, one can make use
of noiseless, (initialization) protectable, or error-correcting subsystems. We
give an explicit algorithm for finding optimal noiseless subsystems. Finding
optimal protectable or error-correcting subsystems is in general difficult.
Verifying that a subsystem is error-correcting involves only linear algebra. We
discuss the verification problem for protectable subsystems and reduce it to a
simpler version of the problem of finding error-detecting codes.Comment: 17 page
An Efficient Hybrid Algorithm for the Separable Convex Quadratic Knapsack Problem
This article considers the problem of minimizing a convex, separable quadratic function subject to a knapsack constraint and a box constraint. An algorithm called NAPHEAP has been developed to solve this problem. The algorithm solves the Karush-Kuhn-Tucker system using a starting guess to the optimal Lagrange multiplier and updating the guess monotonically in the direction of the solution. The starting guess is computed using the variable fixing method or is supplied by the user. A key innovation in our algorithm is the implementation of a heap data structure for storing the break points of the dual function and computing the solution of the dual problem. Also, a new version of the variable fixing algorithm is developed that is convergent even when the objective Hessian is not strictly positive definite. The hybrid algorithm NAPHEAP that uses a Newton-type method (variable fixing method, secant method, or Newton's method) to bracket a root, followed by a heap-based monotone break point search, can be faster than a Newton-type method by itself, as demonstrated in the numerical experiments
Large Fourier transforms never exactly realized by braiding conformal blocks
Fourier transform is an essential ingredient in Shor's factoring algorithm.
In the standard quantum circuit model with the gate set \{\U(2),
\textrm{CNOT}\}, the discrete Fourier transforms , can be realized exactly by
quantum circuits of size , and so can the discrete
sine/cosine transforms. In topological quantum computing, the simplest
universal topological quantum computer is based on the Fibonacci
(2+1)-topological quantum field theory (TQFT), where the standard quantum
circuits are replaced by unitary transformations realized by braiding conformal
blocks. We report here that the large Fourier transforms and the discrete
sine/cosine transforms can never be realized exactly by braiding conformal
blocks for a fixed TQFT. It follows that approximation is unavoidable to
implement the Fourier transforms by braiding conformal blocks
On the Invariants of Towers of Function Fields over Finite Fields
We consider a tower of function fields F=(F_n)_{n\geq 0} over a finite field
F_q and a finite extension E/F_0 such that the sequence
\mathcal{E):=(EF_n)_{n\goq 0} is a tower over the field F_q. Then we deal with
the following: What can we say about the invariants of \mathcal{E}; i.e., the
asymptotic number of places of degree r for any r\geq 1 in \mathcal{E}, if
those of F are known? We give a method based on explicit extensions for
constructing towers of function fields over F_q with finitely many prescribed
invariants being positive, and towers of function fields over F_q, for q a
square, with at least one positive invariant and certain prescribed invariants
being zero. We show the existence of recursive towers attaining the
Drinfeld-Vladut bound of order r, for any r\geq 1 with q^r a square. Moreover,
we give some examples of recursive towers with all but one invariants equal to
zero.Comment: 23 page
On Haagerup's list of potential principal graphs of subfactors
We show that any graph, in the sequence given by Haagerup in 1991 as that of
candidates of principal graphs of subfactors, is not realized as a principal
graph except for the smallest two. This settles the remaining case of a
previous work of the first author.Comment: 19 page
Observation of a 4ΣHe Bound State in the H4e(K−,π−) reaction at 600MeV/c
We have observed a clear peak below the Σ+-production threshold in the 4He(K−,π−) reaction at 600MeV/c and θKπ=4∘. This is confirmation of the existence of the bound state of 4ΣHe, which was reported in the 4He(stoppedK−,π−) reaction. As in the case of stopped kaons, no such peak was found in the 4He(K−,π+) spectrum. Quantitatively reliable parameters for this level have been established. The binding energy and the width of the bound state are 4.4±0.3(stat)±1(syst) MeV and 7.0±0.7(stat)+1.2−0.0(syst) MeV, respectively
Prospect of Studying Hard X- and Gamma-Rays from Type Ia Supernovae
We perform multi-dimensional, time-dependent radiation transfer simulations
for hard X-ray and gamma-ray emissions, following radioactive decays of 56Ni
and 56Co, for two-dimensional delayed detonation models of Type Ia supernovae
(SNe Ia). The synthetic spectra and light curves are compared with the
sensitivities of current and future observatories for an exposure time of 10^6
seconds. The non-detection of the gamma-ray signal from SN 2011fe at 6.4 Mpc by
SPI on board INTEGRAL places an upper limit for the mass of 56Ni of \lesssim
1.0 Msun, independently from observations in any other wavelengths. Signals
from the newly formed radioactive species have not been convincingly measured
yet from any SN Ia, but the future X-ray and gamma-ray missions are expected to
deepen the observable horizon to provide the high energy emission data for a
significant SN Ia sample. We predict that the hard X-ray detectors on board
NuStar (launched in 2012) or ASTRO-H (scheduled for launch in 2014) will reach
to SNe Ia at \sim15 Mpc, i.e., one SN every few years. Furthermore, according
to the present results, the soft gamma-ray detector on board ASTRO-H will be
able to detect the 158 keV line emission up to \sim25 Mpc, i.e., a few SNe Ia
per year. Proposed next generation gamma-ray missions, e.g., GRIPS, could reach
to SNe Ia at \sim20 - 35 Mpc by MeV observations. Those would provide new
diagnostics and strong constraints on explosion models, detecting rather
directly the main energy source of supernova light.Comment: 14 pages, 7 figures, 1 table, accepted for publication in Ap
Snowmass CF1 Summary: WIMP Dark Matter Direct Detection
As part of the Snowmass process, the Cosmic Frontier WIMP Direct Detection
subgroup (CF1) has drawn on input from the Cosmic Frontier and the broader
Particle Physics community to produce this document. The charge to CF1 was (a)
to summarize the current status and projected sensitivity of WIMP direct
detection experiments worldwide, (b) motivate WIMP dark matter searches over a
broad parameter space by examining a spectrum of WIMP models, (c) establish a
community consensus on the type of experimental program required to explore
that parameter space, and (d) identify the common infrastructure required to
practically meet those goals.Comment: Snowmass CF1 Final Summary Report: 47 pages and 28 figures with a 5
page appendix on instrumentation R&
Neutrino masses from new generations
We reconsider the possibility that Majorana masses for the three known
neutrinos are generated radiatively by the presence of a fourth generation and
one right-handed neutrino with Yukawa couplings and a Majorana mass term. We
find that the observed light neutrino mass hierarchy is not compatible with low
energy universality bounds in this minimal scenario, but all present data can
be accommodated with five generations and two right-handed neutrinos. Within
this framework, we explore the parameter space regions which are currently
allowed and could lead to observable effects in neutrinoless double beta decay,
conversion in nuclei and experiments. We
also discuss the detection prospects at LHC.Comment: 28 pages, 4 figures. Version to be published. Some typos corrected.
Improved figures 3 and
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