27,977 research outputs found

    Quantum searching amidst uncertainty

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    Consider a database most of whose entries are marked but the precise fraction of marked entries is not known. What is known is that the fraction of marked entries is 1-X, where X is a random variable that is uniformly distributed in the range (0,X_0) (X_0 is a small number). The problem is to try to select a marked item from the database in a single query. If the algorithm selects a marked item, it succeeds, else if it selects an unmarked item, it makes an error. How low can we make the probability of error? The best possible classical algorithm can lower the probability of error to O((X_0)^2). The best known quantum algorithms for this problem could also only lower the probability of error to O((X_0)^2). Using a recently invented quantum search technique, this paper gives an algorithm that reduces the probability of error to O((X_0)^3). The algorithm is asymptotically optimal.Comment: 10 page

    A More General Quantum Searching Algorithm And the Precise Formula of the Amplitude and the Non-symmetric Effects of Different Rotating Angles

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    This paper presented two general quantum search algorithms. We derived the iterated formulas and the simpler approximate formulas and the precise formula for the amplitude in the desired state. A mathematical proof of Grover's algorithm being optimal among the algorithms with arbitrary phase rotations was given in this paper. This first reported the non-symmetric effects of different rotating angles, and gave the first-order approximate phase condition when rotating angles are different.Comment: 13 pages, misusing tex formatting commands in title, shorted the titles, corrected typos, added the justifications to the section

    From Schr\"odinger's Equation to the Quantum Search Algorithm

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    The quantum search algorithm is a technique for searching N possibilities in only sqrt(N) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from any of the generally known forms of the algorithm. This paper describes these steps, which start by discretizing Schr\"odinger's equation. This paper also provides a self-contained introduction to the quantum search algorithm from a new perspective.Comment: Postscript file, 16 pages. This is a pedagogical article describing the invention of the quantum search algorithm. It appeared in the July, 2001 issue of American Journal of Physics (AJP

    The 55th College Training Detachment of the Army Air Corps Program On the Gettysburg College Campus, 1943-1944

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    The 55th College Training Detachment of the Air Force Cadet Program came to Gettysburg College in 1943. It was a separate program designed to provide educated officers for the Air Corps in the United States Army. These trainees would not only learn military drill, physical training, medical aid and flight skills, but they would also study physics, math, English, history, and geography. They were taught by members of the Gettysburg College staff and housed on campus, in dorms and fraternity houses.Their presence on campus was a constant reminder for regular students that the country was in the midst of a war

    MS-062: George Hay Kain Papers, Class of 1897

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    The collection consists of 46 of George Hay Kain’s letters to his college girlfriend, A. Marjorie Zug, a student at the Women’s College of Baltimore. His letters include commentary on various aspects of college life, including classes, assignments, faculty, fraternity events, sports, commencement, class days, the Preparatory School, and the college publications. The letters date from 1896-1898. Special Collections and College Archives Finding Aids are discovery tools used to describe and provide access to our holdings. Finding aids include historical and biographical information about each collection in addition to inventories of their content. More information about our collections can be found on our website http://www.gettysburg.edu/special_collections/collections/.https://cupola.gettysburg.edu/findingaidsall/1057/thumbnail.jp
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