Computing is a process of mapping from inputs to outputs. A quantum computer performs a physical mapping from initial quantum states to final classical states. This solution mapping process is called the ‘unitary evolution’ of the states of the system.
Solving a problem also represents a mapping from an information input parameter set to an output solution set. NP problems do not allow solutions to be reached under the constraint of serial computing because, as the input parameter space expands, the number of possible mapping pathways to reach an output solution also expands exponentially. NP problem solutions can be more efficiently solved by parallel quantum computing, the power of which increases exponentially at a rate comparable to the exponential increase in the solution set pathways or unitary evolution of the system. This can be modelled as a ‘sum over histories’ or path integral formulation of quantum theory.
As with computing and problem solving processes, evolution also may be thought of as a mapping from the system’s present information state to the target state of the environment. The Action in this case is the integral of the decision paths over an ‘evolutionary field’. The Least Action minimises this integral which is the mathematical process in the author’s theory that drives evolution. The D-Net evolutionary decision network provides a model of this mapping mechanism. The model predicts many different decision paths in the configuration space from input to output, but only a small proportion- the most efficient, are relevant to the system. The other paths are those with the smallest probability of success and can be cancelled out.
Each transition path, including the decision nodes embedded in it, creates a decision history. The sum of these decision histories, provides the evolutionary mapping function and may be integrated to provide the quantum decision integral or sum over histories, for the evolutionary process. Life therefore is an extremely efficient information processor because it incorporates adaptive learning decision pathways that over time maximise the efficiency of the information differential reduction process, within a unitary evolution framework.
In a sense the decision paths become shorter and more efficient, enabling the optimal evolutionary outcome or unitary transform to be achieved at the lowest energy cost,
just as the geodesic in Riemann geometry represents the shortest or most efficient path between two points. There therefore appears to be a strong connection between Riemann geometric functions and evolutionary decision functions, which allows the formulation of a metric to calculate the efficiency of the evolutionary process. In effect the minimal geodesic distance between the information state of the observing system and the target information state of the system’s environment, applying a unitary operator, is equivalent to the minimal number of ‘decision gates or nodes’ and the number of connecting links or steps required to achieve the appropriate adaptation.
In this process the complexity of the system is increased, through the acquisition of additional information, plus greater flexibility and efficiency in resolving the differential, which can therefore be applied to adapt to more complex future environmental challenges.
Such a metric would therefore be a function of the density of decision operations or transformations required to implement the unitary evolutionary transform plus a measure of the efficiency of the information feedback mechanism to keep the evolutionary process on track. In effect, the evolution of the ‘decision matrix’ applied to minimise the information differential, allows the evolution of the system as a whole to be achieved. This in turn could be calculated from Frieden’s Theory combined with existing Quantum Information, Unitary and Network Theory.
Solving a problem also represents a mapping from an information input parameter set to an output solution set. NP problems do not allow solutions to be reached under the constraint of serial computing because, as the input parameter space expands, the number of possible mapping pathways to reach an output solution also expands exponentially. NP problem solutions can be more efficiently solved by parallel quantum computing, the power of which increases exponentially at a rate comparable to the exponential increase in the solution set pathways or unitary evolution of the system. This can be modelled as a ‘sum over histories’ or path integral formulation of quantum theory.
As with computing and problem solving processes, evolution also may be thought of as a mapping from the system’s present information state to the target state of the environment. The Action in this case is the integral of the decision paths over an ‘evolutionary field’. The Least Action minimises this integral which is the mathematical process in the author’s theory that drives evolution. The D-Net evolutionary decision network provides a model of this mapping mechanism. The model predicts many different decision paths in the configuration space from input to output, but only a small proportion- the most efficient, are relevant to the system. The other paths are those with the smallest probability of success and can be cancelled out.
Each transition path, including the decision nodes embedded in it, creates a decision history. The sum of these decision histories, provides the evolutionary mapping function and may be integrated to provide the quantum decision integral or sum over histories, for the evolutionary process. Life therefore is an extremely efficient information processor because it incorporates adaptive learning decision pathways that over time maximise the efficiency of the information differential reduction process, within a unitary evolution framework.
In a sense the decision paths become shorter and more efficient, enabling the optimal evolutionary outcome or unitary transform to be achieved at the lowest energy cost,
just as the geodesic in Riemann geometry represents the shortest or most efficient path between two points. There therefore appears to be a strong connection between Riemann geometric functions and evolutionary decision functions, which allows the formulation of a metric to calculate the efficiency of the evolutionary process. In effect the minimal geodesic distance between the information state of the observing system and the target information state of the system’s environment, applying a unitary operator, is equivalent to the minimal number of ‘decision gates or nodes’ and the number of connecting links or steps required to achieve the appropriate adaptation.
In this process the complexity of the system is increased, through the acquisition of additional information, plus greater flexibility and efficiency in resolving the differential, which can therefore be applied to adapt to more complex future environmental challenges.
Such a metric would therefore be a function of the density of decision operations or transformations required to implement the unitary evolutionary transform plus a measure of the efficiency of the information feedback mechanism to keep the evolutionary process on track. In effect, the evolution of the ‘decision matrix’ applied to minimise the information differential, allows the evolution of the system as a whole to be achieved. This in turn could be calculated from Frieden’s Theory combined with existing Quantum Information, Unitary and Network Theory.
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