P. Hyer. Conjugated operators in quantum algorithms. Preprint, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Sect. 5, this approach suggests implementations which do not require a register of control qubits. A more general formulation of the order finding problem as well as the discrete logarithm problem, and the Abelian stabiliser problem, is the hidden subgroup problem (or the unknown subgroup problem [H]) In the case that G is presented as the product of a finite number of cyclic groups (so G is finitely generated and Abelian) all of these problems are solved by the familiar sequence of a Fourier transform, a function application, and an inverse Fourier transform. In this paper we describe how ....

....take j xi j yi to j xi j y f(x)i, where denotes an appropriate group operation, such as addition modulo N when the second register is used to represent the integers modulo N . Various cases of the hidden subgroup problem are described in [Si] Sh] Ki] BL] Gr] Jo] CEMM] and [H]. We note that [BL] also covers the case that f is not necessarily distinct on each coset (that is, h is not 1 to 1) and this is discussed in the appendix. Finding the order r of an element in a group H of unknown size, or the period r of a function f , is a special case where G = Z and K = rZ. ....

Hyer, P. : Conjugated Operators in Quantum Algorithms. preprint, (1997).

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P. Hyer. Conjugated operators in quantum algorithms. Preprint, 1997.

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HYER, P. 1999. Conjugated operators in quantum algorithms. Phys. Rev. A 59, 5, 3280--3289.

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P. Hyer. Conjugated operators in quantum algorithms. Preprint, 1997.

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