12,088 research outputs found
Algebraic analysis of quantum search with pure and mixed states
An algebraic analysis of Grover's quantum search algorithm is presented for
the case in which the initial state is an arbitrary pure quantum state of n
qubits. This approach reveals the geometrical structure of the quantum search
process, which turns out to be confined to a four-dimensional subspace of the
Hilbert space. This work unifies and generalizes earlier results on the time
evolution of the amplitudes during the quantum search, the optimal number of
iterations and the success probability. Furthermore, it enables a direct
generalization to the case in which the initial state is a mixed state,
providing an exact formula for the success probability.Comment: 13 page
Level-1 jet trigger hardware for the ALICE electromagnetic calorimeter at LHC
The ALICE experiment at the LHC is equipped with an electromagnetic
calorimeter (EMCal) designed to enhance its capabilities for jet measurement.
In addition, the EMCal enables triggering on high energy jets. Based on the
previous development made for the Photon Spectrometer (PHOS) level-0 trigger, a
specific electronic upgrade was designed in order to allow fast triggering on
high energy jets (level-1). This development was made possible by using the
latest generation of FPGAs which can deal with the instantaneous incoming data
rate of 26 Gbit/s and process it in less than 4 {\mu}s.Comment: proceeding of TWEPP-10 at Aachen. 6 pages, 4 figure
Fetching marked items from an unsorted database in NMR ensemble computing
Searching a marked item or several marked items from an unsorted database is
a very difficult mathematical problem. Using classical computer, it requires
steps to find the target. Using a quantum computer, Grover's
algorithm uses steps. In NMR ensemble computing,
Brushweiler's algorithm uses steps. In this Letter, we propose an
algorithm that fetches marked items in an unsorted database directly. It
requires only a single query. It can find a single marked item or multiple
number of items.Comment: 4 pages and 1 figur
A General SU(2) Formulation for Quantum Searching with Certainty
A general quantum search algorithm with arbitrary unitary transformations and
an arbitrary initial state is considered in this work. To serach a marked state
with certainty, we have derived, using an SU(2) representation: (1) the
matching condition relating the phase rotations in the algorithm, (2) a concise
formula for evaluating the required number of iterations for the search, and
(3) the final state after the search, with a phase angle in its amplitude of
unity modulus. Moreover, the optimal choices and modifications of the phase
angles in the Grover kernel is also studied.Comment: 8 pages, 2 figure
Grover's Quantum Search Algorithm for an Arbitrary Initial Mixed State
The Grover quantum search algorithm is generalized to deal with an arbitrary
mixed initial state. The probability to measure a marked state as a function of
time is calculated, and found to depend strongly on the specific initial state.
The form of the function, though, remains as it is in the case of initial pure
state. We study the role of the von Neumann entropy of the initial state, and
show that the entropy cannot be a measure for the usefulness of the algorithm.
We give few examples and show that for some extremely mixed initial states
carrying high entropy, the generalized Grover algorithm is considerably faster
than any classical algorithm.Comment: 4 pages. See http://www.cs.technion.ac.il/~danken/MSc-thesis.pdf for
extended discussio
Identification of a Class of Low-Mass Asymptotic Giant Branch Stars Struggling to Become Carbon Stars in the Magellanic Clouds
We have identified a new class of Asymptotic Giant Branch (AGB) stars in the
Small and Large Magellanic Clouds (SMC/LMC) using optical to infrared
photometry, light curves, and optical spectroscopy. The strong dust production
and long-period pulsations of these stars indicate that they are at the very
end of their AGB evolution. Period-mass-radius relations for the
fundamental-mode pulsators give median current stellar masses of 1.14 M_sun in
the LMC and 0.94 M_sun in the SMC (with dispersions of 0.21 and 0.18 M_sun,
respectively), and models suggest initial masses of <1.5 M_sun and <1.25 M_sun,
respectively. This new class of stars includes both O-rich and C-rich
chemistries, placing the limit where dredge-up allows carbon star production
below these masses. A high fraction of the brightest among them should show S
star characteristics indicative of atmospheric C/O ~ 1, and many will form
O-rich dust prior to their C-rich phase. These stars can be separated from
their less-evolved counterparts by their characteristically red J-[8] colors.Comment: 16 pages, 18 figures, accepted for publication in Ap
The Precise Formula in a Sine Function Form of the norm of the Amplitude and the Necessary and Sufficient Phase Condition for Any Quantum Algorithm with Arbitrary Phase Rotations
In this paper we derived the precise formula in a sine function form of the
norm of the amplitude in the desired state, and by means of he precise formula
we presented the necessary and sufficient phase condition for any quantum
algorithm with arbitrary phase rotations. We also showed that the phase
condition: identical rotation angles, is a sufficient but not a necessary phase
condition.Comment: 16 pages. Modified some English sentences and some proofs. Removed a
table. Corrected the formula for kol on page 10. No figure
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