Boyer, Michel, Gilles Brassard, Peter Hyer and Alain Tapp, \Tight bounds on quantum searching", Fortschritte Der Physik, special issue on quantum computing and quantum cryptography, 1998, Vol. 46, pp. 493 - 505.  Home/Search   Document Not in Database   Summary   Related Articles

....the amplitude of being in a certain subspace of a Hilbert space. The 4 general concept of amplifying the amplitude of a subspace was discovered by Brassard and H yer [4] as a generalization of the boosting technique applied by Grover in his original quantum searching paper [8] Following [4] and [3], we refer to their idea as amplitude ampli cation and detail the ingredients below. Let H denote the Hilbert space representing the state space of a quantum system. Every Boolean function : Z f0; 1g induces a partition of H into a direct sum of two subspaces, a good subspace and a bad ....

....knowledge about a , which itself depends on a. The two extreme cases are when we know the exact value of a, and when we have no prior knowledge about a whatsoever. Suppose the value of a is known. If a 0, then by letting m = b =4 a c, we have that sin 2 ( 2m 1) a ) 1 a, as shown in [3]. The next theorem is immediate. Theorem 2 (Quadratic speedup) Let A be any quantum algorithm that uses no measurements, and let : Z f0; 1g be any Boolean function. Let a the initial success probability of A. Suppose a 0, and set m = b =4 a c, where a is de ned so that sin 2 ( a ) a ....

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Boyer, Michel, Gilles Brassard, Peter Hyer and Alain Tapp, \Tight bounds on quantum searching", Fortschritte Der Physik, special issue on quantum computing and quantum cryptography, 1998, Vol. 46, pp. 493 - 505.

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