Quantum Neural Machine Learning: Theory and Experiments DOI: http://dx.doi.org/10.5772/intechopen.84149

formalism, that is, they agree with the formalism and mathematical methods of quantum mechanics and, therefore, cannot be tested using just the formalism.

the formalism, instead of assuming it as a postulate.

Artificial Intelligence - Applications in Medicine and Biology

Everett in [8] regarding Born's rule.

dynamics.

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In the case of Cramer, his proposed transactional interpretation (TI) of quantum mechanics [7] considers a probabilistic selection in terms of a quantum handshake (Cramer's transaction), where there is a sequential hierarchical selection for a quantum handshake linking the beginning and endpoint of the quantum dynamics, where each alternative is evaluated probabilistically for the formation of a quantum handshake or not; if no handshake is selected for a given alternative, the quantum dynamics proceeds to the next alternative. In each case, the probability for a quantum handshake is equal to the echo intensity, thus deriving Born's rule from within

Everett [8] assumed that all alternatives for a quantum system are actualized simultaneously in different cosmic branches. This led to the many worlds interpretation (MWI). MWI's proposal is, thus, that reality is multidimensional and the formalism is considered to be describing such a multidimensional reality that is a single Cosmos with many worlds (many branching lines). This conjecture cannot be tested empirically; it is consistent with the formalism and agrees with the predictions of quantum mechanics. Namely, the statistical measure associated with repeated experiments made on quantum systems tends to coincide with the echo intensities since the echo intensities coincide with the existence intensity of each world, recovering a statistical measure upon repeated experiments, as argued by

Bohm initially worked on the pilot wave model for quantum mechanics but just as a first approximation. Indeed, in [9], the author addressed the pilot wave model

Gonçalves in [6] addressed the relation between the echo and Bohm's proposal

In this interpretation, the echo is associated with a dynamics of a quantum field for the evaluation of each alternative; the probing and response dynamics, thus, play a fundamental role, allowing a quantum field, any quantum field, to compute each alternative in parallel, leading to an echo associated with each alternative.

As argued in [6], the intensity (modulated) echoes would, thus, have a functional

This quantum computational dynamics, present in quantum mechanics' formalism, works as a basic form of quantum "learning" dynamics, where the quantum field "learns" about each alternative in the probe (forward propagating) and response (back propagating) dynamics and, then, the field's lines of force are formed along the echoes resulting from the encounters of matching probe and response vectors, with a force intensity that matches the corresponding echo's intensity; the field then follows one of these lines of force with a probability that coincides with the echo

role as signalizers of an order to be risen (in the QUANN case, this order corresponds to a specific quantum neural firing pattern); the field's quantum and subquantum levels would, then, work in tandem, mobilizing the forces needed to make rise one specific alternative, and the resulting field lines of force, therefore,

recovering the Bohmian concept of quantum force [9, 10].

coincide, in their intensities, with the echo intensities.

as a first approximation but then criticized it, in particular, in regard to the assumption of a particle being separate from the field; even more, in [9], Bohm defended that, at a lower level, the particle does not move as a permanently existing entity, but is formed in a random way by suitable concentrations of the field's energy. Furthermore, he considered that any quantum field was characterized by a nonlocal dynamics, and that the equations of quantum mechanics were just an approximation, an average that emerged at the quantum level, proposing the concept of quantum force and hypothesizing the existence of a subquantum level, so that both the quantum and subquantum levels play a fundamental role in the field's intensity, so that the following of a given line of force is similar to a bifurcation dynamics where the field will follow, stochastically, one of the branches with a probability that coincides with the force intensity associated with each branch [6].

There is a consequence that comes from assuming the Bohmian framework, namely, from the Bohm's conjecture that a subquantum level randomness averages out at the quantum level, but may lead to small deviations from the theoretical probabilities [9, 10]; if such a conjecture holds, then deviations in quantum physical experiments with actual quantum computers may always take place, such that, even if we were to reduce the interaction with the environment to zero (or close to zero), we could still have deviations due to subquantum level fluctuations, so that the field would tend to follow the lines of force with probabilities that would hold on average but with some deviations that might occur in each case.

While Bohm's proposal is potentially testable, at the present stage of scientific and technological development, we have not yet found a way to test the subquantum proposal regarding quantum physical systems, and, in particular, to test, empirically, the possibility that deviations from the main lines of force that agree with a theory's prediction are not due to environmental noise and, rather, to subquantum level fluctuations.

All main interpretations, as reviewed above, agree with quantum mechanics' general predictions, even Bohm, who considers that the predictions will hold empirically on average, therefore, the interpretations do not have, at present, a direct consequence on the results of technological implementation of quantum computers, as long as one is not dealing with fundamental ontological issues regarding the computational nature of quantum fields, but rather with the technological application of quantum algorithms, one is free to choose any interpretation since it is consistent with the main formalism and results.

We consider, nonetheless, that future research directions on Bohm's conjectural line may prove fruitful both at a theoretical and technological level, concerning the issue of quantum errors. This point, however, goes beyond the current chapter's scope. The results that follow, as of any work using the formalism of quantum mechanics, hold for any interpretation of the theory. However, having made that point, we will return to Bohm's conjecture regarding some of the results obtained in the next section, regarding the issue of quantum computing errors.
