Foundations of Physics 48 (3):333-354 (2018)

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Abstract
The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete. We complete it in three steps: extending the representation to the process of setting the problem, relativizing the extended representation to the problem solver to whom the problem setting must be concealed, and symmetrizing the relativized representation for time reversal to represent the reversibility of the underlying physical process. The third steps projects the input state of the representation, where the problem solver is completely ignorant of the setting and thus the solution of the problem, on one where she knows half solution. Completing the physical representation shows that the number of computation steps required to solve any oracle problem in an optimal quantum way should be that of a classical algorithm endowed with the advanced knowledge of half solution.
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DOI 10.1007/s10701-018-0146-3
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Algorithms for Quantum Computation: Discrete Logarithms and Factoring.P. Shor - 1994 - Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science:124-134.
On the Role of Entanglement in Quantum-Computational Speed-Up.Richard Jozsa & Noah Linden - 2003 - Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 459:2011--2032.

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