Speedup of Iterated Quantum Search by Parallel Performance

Given a sequence f1(x1), f2(x1, x2), . . . , fk(x1, . . . , xk) of Boolean functions, each of which fi takes the value 1 in a single point of the form x 0 , x 0 , . . . , x 0 , i = 1,2, . . . , k. A length of all x 0 is n, N = 2 n . It is shown how to find x 0 (k ≥ 2) using kπ √ N 4 √ 2 simultaneous evaluations of functions of the form fi, fi+1 with an error probability of order k/ √ N which is √ 2 times as fast as by the k sequential applications of Grover algorithm for the quantum search. Evolutions of amplitudes in parallel quantum computations are approximated by systems of linear differential equations. Some advantage of simultaneous evaluations of all f1, . . . fk are discussed.

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