Quantum search algorithms on a regular lattice

Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level-splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behaviour for the search time and the localisation probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions

Quantum Mechanics helps in searching for a needle in a haystack

Quantum mechanics can speed up a range of search applications over unsorted data. For example imagine a phone directory containing N names arranged in completely random order. To find someone's phone number with a probability of 50%, any classical algorithm (whether deterministic or probabilistic) will need to access the database a minimum of O(N) times. Quantum mechanical systems can be in a superposition of states and simultaneously examine multiple names. By properly adjusting the phases of various operations, successful computations reinforce each other while others interfere randomly. As a result, the desired phone number can be obtained in only O(sqrt(N)) accesses to the database.Comment: Postscript, 4 pages. This is a modified version of the STOC paper (quant-ph/9605043) and is modified to make it more comprehensible to physicists. It appeared in Phys. Rev. Letters on July 14, 1997. (This paper was originally put out on quant-ph on June 13, 1997, the present version has some minor typographical changes

Observation of tunable exchange bias in Sr2_2YbRuO6_6

The double perovskite compound, Sr$_{2}$YbRuO$_{6}$, displays reversal in the orientation of magnetic moments along with negative magnetization due to an underlying magnetic compensation phenomenon. The exchange bias (EB) field below the compensation temperature could be the usual negative or the positive depending on the initial cooling field. This EB attribute has the potential of getting tuned in a preselected manner, as the positive EB field is seen to crossover from positive to negative value above $T_{\mathrm{comp}}$.Comment: 4 Pages, 4 Figure

Noise in Grover's Quantum Search Algorithm

Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude in Grover's algorithm. We study the algorithm's intrinsic robustness when no quantum correction codes are used, and evaluate how much noise the algorithm can bear with, in terms of the size of the phone book and a desired probability of finding the correct result. The algorithm loses efficiency when noise is added, but does not slow down. We also study the maximal noise under which the iterated quantum algorithm is just as slow as the classical algorithm. In all cases, the width of the allowed noise scales with the size of the phone book as N^-2/3.Comment: 17 pages, 2 eps figures. Revised version. To be published in PRA, December 199

Energy and Efficiency of Adiabatic Quantum Search Algorithms

We present the results of a detailed analysis of a general, unstructured adiabatic quantum search of a data base of $N$ items. In particular we examine the effects on the computation time of adding energy to the system. We find that by increasing the lowest eigenvalue of the time dependent Hamiltonian {\it temporarily} to a maximum of $\propto \sqrt{N}$, it is possible to do the calculation in constant time. This leads us to derive the general theorem which provides the adiabatic analogue of the $\sqrt{N}$ bound of conventional quantum searches. The result suggests that the action associated with the oracle term in the time dependent Hamiltonian is a direct measure of the resources required by the adiabatic quantum search.Comment: 6 pages, Revtex, 1 figure. Theorem modified, references and comments added, sections introduced, typos corrected. Version to appear in J. Phys.

New Samarium and Neodymium based admixed ferromagnets with near zero net magnetization and tunable exchange bias field

Rare earth based intermetallics, SmScGe and NdScGe, are shown to exhibit near zero net magnetization with substitutions of 6 to 9 atomic percent of Nd and 25 atomic percent of Gd, respectively. The notion of magnetic compensation in them is also elucidated by the crossover of zero magnetization axis at low magnetic fields (less than 103 Oe) and field-induced reversal in the orientation of the magnetic moments of the dissimilar rare earth ions at higher magnetic fields. These magnetically ordered materials with no net magnetization and appreciable conduction electron polarization display an attribute of an exchange bias field, which can be tuned. The attractively high magnetic ordering temperatures of about 270 K, underscore the importance of these materials for potential applications in spintronics.Comment: 6 page text + 5 figure

Optimization of Partial Search

Quantum Grover search algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block) containing the target item even faster, this is partial search. A partial search algorithm was recently suggested by Grover and Radhakrishnan. Here we optimize it. Efficiency of the search algorithm is measured by number of queries to the oracle. The author suggests new version of Grover-Radhakrishnan algorithm which uses minimal number of queries to the oracle. The algorithm can run on the same hardware which is used for the usual Grover algorithm.Comment: 5 page