Dong Pyo Chi and Jingsoo Kim, "Quantum database searching by a single query", to appear in Proc. of the 1st NASA Int. Conf. on Quantum Computing and Quantum Communication, Lecture Notes in Computer Science (1998).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a with sin 2 (f a ) When we know a we know exactly how many applications of G we should use to search for elements of X 1 . We can also alter G slightly so that the ideal number, M , of applications is an integer, making the search exact. This was first done for M = 1 in [7] and later in [11], by altering the phase shifts in U 0 and U f . This method is also used for any M 0 in [9] and [8] Another simple method is to modify A and f so that a is slightly smaller but can be amplified to 1 with an integer number of iterations of G (see [9] 20] or [8] In the next section we ....

Dong Pyo Chi and Jingsoo Kim, "Quantum database searching by a single query", to appear in Proc. of the 1st NASA Int. Conf. on Quantum Computing and Quantum Communication, Lecture Notes in Computer Science (1998).

....a good solution with certainty, we also apply d me iterations of amplitude ampli cation, but now we slow down the speed of the 11 very last iteration only, as opposed to of all iterations as in the rst method. For the case m 1, this second method has also been suggested by Chi and Kim [6]. We start by applying the operator Q(A; with = a number of b mc times to the initial state j i = Aj0i. By Equation 8, this produces the superposition 1 p a sin (2b mc 1) a j 1 i 1 p 1 a cos (2b mc 1) a j 0 i: Then, we apply operator Q one more time, ....

Chi, Dong{Pyo and Jinsoo Kim, \Quantum database searching by a single query", Lecture at First NASA International Conference on Quantum Computing and Quantum Communications, Palm Springs, February 1998. 31

....and the same strategy of Section 5 to search for a solution when we do not know a. When we do know a we know exactly how many applications of G we should use. We can also alter G so that the ideal number, M , of applications is an integer, making the search exact (this is done for M = 1 in [4] and [6]) Here we will describe another way of doing it 6 . Step 1: Knowing a we know a and a , so define k = d a = a e. Step 2: Solve for a 0 a such that k = a 0 = a 0 . 6 This fact was pointed out to me independently by H. Buhrman, W. van Dam, and P. H yer in November 1997. Step ....

Dong Pyo Chi and Jingsoo Kim, "Quantum database searching by a single query", to appear in Proceedings of the 1st NASA International Conference on Quantum Computing and Quantum Communications, (1998), (http://xxx.lanl.gov/abs/quant-ph/9708005).

.... 2 m0 = 2a(1 Gamma Re(OE) and so that (1 Gamma OE)ak m0 Gamma ( 1 Gamma OE)a OE) m0 vanishes. Going through the algebra and applying Lemma 3 shows that this produces a good solution with certainty. For the case m 0 = 0, this second method was independently discovered by Chi and Kim [7]. Suppose now that the value of a is not known. In Section 4, we discuss techniques for finding a good estimate of a, after which one then can apply a weakened version of Theorem 2 to find a good solution. Another idea is to try to find a good solution without prior computation of an estimate of ....

Chi, Dong-Pyo and Jinsoo Kim, "Quantum database searching by a single query", Lecture at First NASA International Conference on Quantum Computing and Quantum Communications, Palm Springs, February 1998.

...., that is, marking the states by multiplying e #i 2 = i and using the # 2 phase dioeusion transform, the solution can be found with certainty after a single iteration (see [17] Actually, by Theorem 3.7.1 it is possible to nd a solution in a single query for all t # N 4. See Chi and Kim [19] for summaries. Theorem 3.9.2. Let t # [ N 4 , N ] Take # in [# 3, 5# 3] such that cos # = 1 N 2t # [ 1, 1 2 ] Then we have G F,# #(k 0 , k 0 )# = # # #( e i# 1)k 0 , 0) # . When t is unknown we can use the following algorithm [16, 35] Algorithm 3.9.2 (General quantum ....

D. P. Chi and J. Kim, Quantum database searching by a single query, Los Alamos e-print archive quant-ph/9708005, Los Alamos, 1997.

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