Quantum computation and the physical computation level of biological information processing

On the basis of introspective analysis, we establish a crucial requirement for the physical computation basis of consciousness: it should allow processing a significant amount of information together at the same time. Classical computation does not satisfy the requirement. At the fundamental physical level, it is a network of two body interactions, each the input-output transformation of a universal Boolean gate. Thus, it cannot process together at the same time more than the three bit input of this gate - many such gates in parallel do not count since the information is not processed together. Quantum computation satisfies the requirement. At the light of our recent explanation of the speed up, quantum measurement of the solution of the problem is analogous to a many body interaction between the parts of a perfect classical machine, whose mechanical constraints represent the problem to be solved. The many body interaction satisfies all the constraints together at the same time, producing the solution in one shot. This shades light on the physical computation level of the theories that place consciousness in quantum measurement and explains how informations coming from disparate sensorial channels come together in the unity of subjective experience. The fact that the fundamental mechanism of consciousness is the same of the quantum speed up, gives quantum consciousness a potentially enormous evolutionary advantage.Comment: 13 page

Quantum algorithms know in advance 50% of the solution they will find in the future

Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find in the future. In fact they can be represented as the sum of all the possible histories of a respective "advanced information classical algorithm". This algorithm, given the advanced information (50% of the bits encoding the problem solution), performs the operations (oracle's queries) still required to identify the solution. Each history corresponds to a possible way of getting the advanced information and a possible result of computing the missing information. This explanation of the quantum speed up has an immediate practical consequence: the speed up comes from comparing two classical algorithms, with and without advanced information, with no physics involved. This simplification could open the way to a systematic exploration of the possibilities of speed up.Comment: The example of new quantum speed up that was just outlined in the previous version (finding the character of a permutation) is fully deployed in the present version. There are minor distributed changes to the writin

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

Cosmic ray secular variations in terrestrial records and aurorae

The rediscovery that the Sun and the solar wind can undergo important changes on historical time scales has brought into question the stability of the cyclic behavior of past time series of solar and solar-terrestrial origin. It was found by Vector Fourier analysis that the solar 11 year cycle is present in the series of 10Be, delta 180, in ice cores and of thermoluminescence (TL) in sea sediments during the last Millennia with a frequency modulation, related to the Sun behavior, as tested by comparison with the Sunspot number R sub z series. It was shown that the cyclogram of the series of yearly Aurorae from 1721 to 1979 linear-regression-corrected-for-R sub z is straight for the periodicity zeta=11,1y, which indicates that such periodicity is constant in time corresponding to the only line present in the 11y band. The maxima of this component appear at the same time together with the high speed solar wind streams taking place in coronal holes situated in high heliolatitudes. It is evidenced that the 11 year cycle has undergone frequency oscillations on a time scale of two centuries, although it is very difficult to determine the periodicities with high accuracy

The global and persistent millennial-scale variability in the thermoluminescence profiles of shallow and deep Mediterranean sea cores

In this paper we present the thermoluminescence (TL) profile in the last 7500 y, measured in the upper part of the deep Tyrrhenian sea core CT85-5. This core was dated with tephroanalysis and radiocarbon techniques: a constant sedimentation rate (10 cm/ky) was found up to 200 cm. The sampling interval adopted for obtaining the TL profile is 2.5 mm, corresponding to 25 y. Using different spectral-analysis methods, we show the presence of a millennial-scale variability, corresponding to an average period of about 1315 y. This oscillation has been noted also in other climatic indices measured in North Atlantic sea sediment cores and in the Greenland GISP2 ice core. This result indicates that this millennial oscillation is the expression of climate changes of worldwide extent. We show that this millennial periodicity persisted during the last deglaciation. The transition to Holocene was determined in our core by the oxygen isotope ratio d 18O measured in Globigerina bulloides. The fact that the observed TL changes do not have a local character is also suggested by the excellent agreement between this deep sea TL profile of the uppermost part of the core and the TL profile measured in the shallow Ionian sea GT89-3 core over the last 2500 y, with a time resolution of 3.096 y

The sunspot cycle recorded in the thermoluminescence profile of the GT89/3 Ionian sea core

We measured the thermoluminescence (TL) depth profile of the GT89O3 shallow-water Ionian sea core. This profile has been transformed into a time series using the accurate sedimentation rate previously determined by radiometric and tephroanalysis methods. The TL measurements were performed in samples of equal thickness of 2 mm, corresponding to a time interval of 3.096 y. The TL time series spans A1800 y. The DFT power spectral densities in the decadal periodicity range of this TL series show significant periodicities at 10.7, 11.3 and 12 y closely similar to the periodicities present in the sunspot number series. These results confirm that the TL signal in recent sea sediments faithfully records the solar variability, as we previously proposed

22 year cycle in the planktonic 18 of a shallow-water Ionian sea core

The d18 O profile of Globigerinoides ruber was measured in the GT90/3 Ionian sea core between 1205 and 1898 AD. The high temporal resolution of 3.87 y allowed us to determine the presence in the time series of an 11 y component with an amplitude of 0.07‰, at significance level of 99% (by Monte Carlo singular spectrum analysis, MC-SSA). Here we focus attention on the 22 y periodicity in the time series and we show that SSA principal components (PCs) 15 and 16 carry this oscillation, in phase with the Hale solar cycle, obtained by inverting the odd cycles of the sunspot number series. This result shows that the even and odd Schwabe cycles do not have the same influence on this climatic record