Quantum Multi-object Search Algorithm with the Availability of Partial Information

Consider the unstructured search of an unknown number l of items in a large unsorted database of size N. The multi-object quantum search algorithm consists of two parts. The first part of the algorithm is to generalize Grover's single-object search algorithm to the multi-object case and the second part is to solve a counting problem to determine l. In this paper, we study the multi-object quantum search algorithm (in continuous time), but in a more structured way by taking into account the availability of partial information. The modeling of available partial information is done simply by the combination of several prescribed, possibly overlapping, information sets with varying weights to signify the reliability of each set. The associated statistics is estimated and the algorithm efficiency and complexity are analyzed. Our analysis shows that the search algorithm described here may not be more efficient than the unstructured (generalized) multi-object Grover search if there is ``misplaced confidence''. However, if the information sets have a ``basic confidence'' property in the sense that each information set contains at least one search item, then a quadratic speedup holds on a much smaller data space, which further expedite the quantum search for the first item.Comment: 17 pages, 1 figur

4. generációs mobil rendszerek kutatása = Research on 4-th Generation Mobile Systems

A 3G mobil rendszerek szabványosítása a végéhez közeledik, legalábbis a meghatározó képességek tekintetében. Ezért létfontosságú azon technikák, eljárások vizsgálata, melyek a következő, 4G rendszerekben meghatározó szerepet töltenek majd be. Több ilyen kutatási irányvonal is létezik, ezek közül projektünkben a fontosabbakra koncentráltunk. A következőben felsoroljuk a kutatott területeket, és röviden összegezzük az elért eredményeket. Szórt spektrumú rendszerek Kifejlesztettünk egy új, rádiós interfészen alkalmazható hívásengedélyezési eljárást. Szimulációs vizsgálatokkal támasztottuk alá a megoldás hatékonyságát. A projektben kutatóként résztvevő Jeney Gábor sikeresen megvédte Ph.D. disszertációját neurális hálózatokra épülő többfelhasználós detekciós technikák témában. Az elért eredmények Imre Sándor MTA doktori disszertációjába is beépültek. IP alkalmazása mobil rendszerekben Továbbfejlesztettük, teszteltük és általánosítottuk a projekt keretében megalkotott új, gyűrű alapú topológiára épülő, a jelenleginél nagyobb megbízhatóságú IP alapú hozzáférési koncepciót. A témakörben Szalay Máté Ph.D. disszertációja már a nyilvános védésig jutott. Kvantum-informatikai módszerek alkalmazása 3G/4G detekcióra Új, kvantum-informatikai elvekre épülő többfelhasználós detekciós eljárást dolgoztunk ki. Ehhez új kvantum alapú algoritmusokat is kifejlesztettünk. Az eredményeket nemzetközi folyóiratok mellett egy saját könyvben is publikáltuk. | The project consists of three main research directions. Spread spectrum systems: we developed a new call admission control method for 3G air interfaces. Project member Gabor Jeney obtained the Ph.D. degree and project leader Sandor Imre submitted his DSc theses from this area. Application of IP in mobile systems: A ring-based reliable IP mobility mobile access concept and corresponding protocols have been developed. Project member Máté Szalay submitted his Ph.D. theses from this field. Quantum computing based solutions in 3G/4G detection: Quantum computing based multiuser detection algorithm was developed. Based on the results on this field a book was published at Wiley entitled: 'Quantum Computing and Communications - an engineering approach'

Quantum Computing: Pro and Con

I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; I discuss recently developed fault-tolerant procedures that enable a quantum computer with noisy gates to perform reliably. Quantum computing hardware is still in its infancy; I comment on the specifications that should be met by future hardware. Over the past few years, work on quantum computation has erected a new classification of computational complexity, has generated profound insights into the nature of decoherence, and has stimulated the formulation of new techniques in high-precision experimental physics. A broad interdisciplinary effort will be needed if quantum computers are to fulfill their destiny as the world's fastest computing devices. (This paper is an expanded version of remarks that were prepared for a panel discussion at the ITP Conference on Quantum Coherence and Decoherence, 17 December 1996.)Comment: 17 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor correction

Models to Reduce the Complexity of Simulating a Quantum Computer

Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation is a useful tool for determining the feasibility of quantum computers in the presence of errors. The size of a quantum computer that can be simulat ed is small because faithfully modeling a quantum computer requires an exponential amount of storage and number of operations. In this paper we define simulation models to study the feasibility of quantum computers. The most detailed of these models is based directly on a proposed imple mentation. We also define less detailed models which are exponentially less complex but still pro duce accurate results. Finally we show that the two different types of errors, decoherence and inaccuracies, are uncorrelated. This decreases the number of simulations which must be per formed.Comment: 25 page

Evolutionary Computation in Coded Communications: an Implementation of Viterbi Algorithm

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Resource Evaluation of Quantum Linear Systems Algorithm for Application to Electromagnetic Scattering Problems

Current limitations in quantum computing technology does not allow for very large applications of quantum algorithms, and it is the nature of quantum algorithms not only to be able to solve problems of interest much more quickly than classical means but also to do so with less resources which makes them so promising! One such problem of interest is the application of the Quantum Linear Systems Algorithm, along with a few other subroutines, to the calculation of an electromagnetic scattering cross-section via finite element methods. This work composes a resource analysis of the algorithm as well as required subroutines and details the primary contributors to the resources involved as well as methods to decrease these resource requirements

Decoherence in quantum walks - a review

The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, led rapidly to several new quantum algorithms. These all follow unitary quantum evolution, apart from the final measurement. Since logical qubits in a quantum computer must be protected from decoherence by error correction, there is no need to consider decoherence at the level of algorithms. Nonetheless, enlarging the range of quantum dynamics to include non-unitary evolution provides a wider range of possibilities for tuning the properties of quantum walks. For example, small amounts of decoherence in a quantum walk on the line can produce more uniform spreading (a top-hat distribution), without losing the quantum speed up. This paper reviews the work on decoherence, and more generally on non-unitary evolution, in quantum walks and suggests what future questions might prove interesting to pursue in this area.Comment: 52 pages, invited review, v2 & v3 updates to include significant work since first posted and corrections from comments received; some non-trivial typos fixed. Comments now limited to changes that can be applied at proof stag