The quantum speed up as advanced knowledge of the solution

With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple two line argument for this without having to describe the details of the search algorithm". The answer provided in this work is: "because any quantum algorithm takes the time taken by a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem". This empirical fact, unnoticed so far, holds for both quadratic and exponential speed ups and is theoretically justified in three steps: (i) once the physical representation is extended to the production of the problem on the part of the oracle and to the final measurement of the computer register, quantum computation is reduction on the solution of the problem under a relation representing problem-solution interdependence, (ii) the speed up is explained by a simple consideration of time symmetry, it is the gain of information about the solution due to backdating, to before running the algorithm, a time-symmetric part of the reduction on the solution; this advanced knowledge of the solution reduces the size of the solution space to be explored by the algorithm, (iii) if I is the information acquired by measuring the content of the computer register at the end of the algorithm, the quantum algorithm takes the time taken by a classical algorithm that knows in advance 50% of I, which brings us to the initial statement.Comment: 23 pages, to be published in IJT

The forms of repetition in social and environmental reports: insights from Hume's notion of ?impressions?

This paper focuses on the use of repetition, both in narrative and visual forms, in social and environmental reports. It investigates the forms of repetition as a rhetorical device adopted by the preparer of a social and environmental report in helping the process of knowledge acquisition, as outlined by Hume (1739). Drawing from Hume?s (1739) philosophical idea of an ?impression?, and the work of Davison (2014a) we classify repetitions into ?identical?, ?similar? and ?accumulated? forms. It is argued that the rationale for distinguishing between the different forms of repetition can be linked to their different potential or intensity in acting on different stimuli with a view to enhance learning. The empirical element of this study is based on the stand-alone social and environmental reports of a sample of 86 cooperative banks in Northern Italy; the analysis of these reports indicates that repetition is widespread and that cooperative banks use all forms of repetition, albeit to a varying extent within the different reported themes. The paper contributes to the literature by offering an alternative interpretation of repetition using an interdisciplinary perspective and by providing new insights on social and environmental reporting practices in the cooperative banking sector