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 $O(N=2^n)$ steps to find the target. Using a quantum computer, Grover's algorithm uses $O(\sqrt{N=2^n})$ steps. In NMR ensemble computing, Brushweiler's algorithm uses $\log N$ 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