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 50% advanced information rule of the quantum algorithms

The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function through function evaluation. This is the typical problem addressed by the quantum algorithms. In former theoretical work, we showed that a quantum algorithm requires the number of function evaluations of a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem. Here we check that this 50% rule holds for the main quantum algorithms. In the structured problems, a classical algorithm with the advanced information, to identify the missing information should perform one function evaluation. The speed up is exponential since a classical algorithm without advanced information should perform an exponential number of function evaluations. In unstructured database search, a classical algorithm that knows in advance 50% of the n bits of the database location, to identify the n/2 missing bits should perform Order(2 power n/2) function evaluations. The speed up is quadratic since a classical algorithm without advanced information should perform Order(2 power n) function evaluations. The 50% rule identifies the problems solvable with a quantum sped up in an entirely classical way, in fact by comparing two classical algorithms, with and without the advanced information.Comment: 18 pages, submitted with minor changes to the International Journal of Theoretical Physic

Stochastic thermodynamics of holonomic systems

International audienc

Acidogenic fermentation of starchy agroindustrial residues: metabolic profile & influence of thermal pretreatment

Volatile fatty acids (VFAs) are short-chain carboxylates consisting of six or fewer carbon atoms. They are produced either synthetically from fossil resources or as metabolic intermediates in the acidogenic fermentation (acidogenesis) step of anaerobic digestion process. These carboxylates are platform chemicals and have a wide range of applications such as in the production of biochemicals, bioplastics, biofuels, green solvents and biological nutrient removal [1]. The environmental and geopolitical impacts of the use of fossil resources as the raw materials have renewed the interest in bioresources such as agricultural and agro-industrial residues

Modelling Stem Cells Lineages with Markov Trees

A variational Bayesian EM with smoothed probabilities algorithm for hidden Markov trees (HMT) is proposed for incomplete tree structured data. The full posterior of the HMT parameters is determined and the underflow problems associated with previous algorithms are eliminated. Example results for the prediction of the types of cells in real stem cell lineage trees are presented