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

Characterization of aerosol associated with enhanced small particle number concentrations in a suburban forested environment

Two elevated particle number/mass growth events associated with Aitken‐mode particles were observed during a sampling campaign (13–29 September 2004) at the Duke University Free‐Air CO2 Enrichment facility, a forested field site located in suburban central North Carolina. Aerosol growth rates between 1.2 and 4.9 nm hr−1 were observed, resulting in net increases in geometric mean diameter of 21 and 37 nm during events. Growth was dominated by addition of oxidized organic compounds. Campaign‐average aerosol mass concentrations measured by an Aerodyne quadrupole aerosol mass spectrometer (Q‐AMS) were 1.9 ± 1.6 (σ), 1.6 ± 1.9, 0.1 ± 0.1, and 0.4 ± 0.4 μg m−3 for organic mass (OM), sulfate, nitrate, and ammonium, respectively. These values represent 47%, 40%, 3%, and 10%, respectively, of the measured submicron aerosol mass. Based on Q‐AMS spectra, OM was apportioned to hydrocarbon‐like organic aerosol (HOA, likely representing primary organic aerosol) and two types of oxidized organic aerosol (OOA‐1 and OOA‐2), which constituted on average 6%, 58%, and 36%, respectively, of the apportioned OM. OOA‐1 probably represents aged, regional secondary organic aerosol (SOA), while OOA‐2 likely reflects less aged SOA. Organic aerosol characteristics associated with the events are compared to the campaign averages. Particularly in one event, the contribution of OOA‐2 to overall OM levels was enhanced, indicating the likelihood of less aged SOA formation. Statistical analyses investigate the relationships between HOA, OOA‐1, OOA‐2, other aerosol components, gas‐phase species, and meteorological data during the campaign and individual events. No single variable clearly controls the occurrence of a particle growth event

Inequalities that test locality in quantum mechanics

Quantum theory violates Bell's inequality, but not to the maximum extent that is logically possible. We derive inequalities (generalizations of Cirel'son's inequality) that quantify the upper bound of the violation, both for the standard formalism and the formalism of generalized observables (POVMs). These inequalities are quantum analogues of Bell inequalities, and they can be used to test the quantum version of locality. We discuss the nature of this kind of locality. We also go into the relation of our results to an argument by Popescu and Rohrlich (Found. Phys. 24, 379 (1994)) that there is no general connection between the existence of Cirel'son's bound and locality.Comment: 5 pages, 1 figure; the argument has been made clearer in the revised version; 1 reference adde

Efficient Scheme for Initializing a Quantum Register with an Arbitrary Superposed State

Preparation of a quantum register is an important step in quantum computation and quantum information processing. It is straightforward to build a simple quantum state such as |i_1 i_2 ... i_n\ket with $i_j$ being either 0 or 1, but is a non-trivial task to construct an {\it arbitrary} superposed quantum state. In this Paper, we present a scheme that can most generally initialize a quantum register with an arbitrary superposition of basis states. Implementation of this scheme requires $O(Nn^2)$ standard 1- and 2-bit gate operations, {\it without introducing additional quantum bits}. Application of the scheme in some special cases is discussed.Comment: 4 pages, 4 figures, accepted by Phys. Rev.

The structure, energy, and electronic states of vacancies in Ge nanocrystals

The atomic structure, energy of formation, and electronic states of vacancies in H-passivated Ge nanocrystals are studied by density functional theory (DFT) methods. The competition between quantum self-purification and the free surface relaxations is investigated. The free surfaces of crystals smaller than 2 nm distort the Jahn-Teller relaxation and enhance the reconstruction bonds. This increases the energy splitting of the quantum states and reduces the energy of formation to as low as 1 eV per defect in the smallest nanocrystals. In crystals larger than 2 nm the observed symmetry of the Jahn-Teller distortion matches the symmetry expected for bulk Ge crystals. Near the nanocrystal's surface the vacancy is found to have an energy of formation no larger than 0.5 to 1.4 eV per defect, but a vacancy more than 0.7 nm inside the surface has an energy of formation that is the same as in bulk Ge. No evidence of the self-purification effect is observed; the dominant effect is the free surface relaxations, which allow for the enhanced reconstruction. From the evidence in this paper, it is predicted that for moderate sized Ge nanocrystals a vacancy inside the crystal will behave bulk-like and not interact strongly with the surface, except when it is within 0.7 nm of the surface.Comment: In Press at Phys. Rev.

Quantum Computing of Classical Chaos: Smile of the Arnold-Schrodinger Cat

We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with moderate imperfections is able to simulate accurately the unstable chaotic classical dynamics for long times. The algorithm can be easily implemented on systems of a few qubits.Comment: revtex, 4 pages, 4 figure

Exponential Gain in Quantum Computing of Quantum Chaos and Localization

We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms. This shows that important physical problems of quantum chaos, localization and Anderson transition can be modelled efficiently on a quantum computer. We also show that a similar algorithm simulates efficiently classical chaos in certain area-preserving maps.Comment: final published versio

Operational improvements of long-term predicted ephemerides of the Tracking and Data Relay Satellites (TDRSs)

Tracking and Data Relay Satellite (TDRS) orbit determination and prediction are supported by the Flight Dynamics Facility (FDF) of the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD). TDRS System (TDRSS)-user satellites require predicted TDRS ephemerides that are up to 10 weeks in length. Previously, long-term ephemerides generated by the FDF included predictions from the White Sands Complex (WSC), which plans and executes TDRS maneuvers. TDRSs typically have monthly stationkeeping maneuvers, and predicted postmaneuver state vectors are received from WSC up to a month in advance. This paper presents the results of an analysis performed in the FDF to investigate more accurate and economical long-term ephemerides for the TDRSs. As a result of this analysis, two new methods for generating long-term TDRS ephemeris predictions have been implemented by the FDF. The Center-of-Box (COB) method models a TDRS as fixed at the center of its stationkeeping box. Using this method, long-term ephemeris updates are made semiannually instead of weekly. The impulse method is used to model more maneuvers. The impulse method yields better short-term accuracy than the COB method, especially for larger stationkeeping boxes. The accuracy of the impulse method depends primarily on the accuracy of maneuver date forecasting