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Quantum Computing-III
What problems are we trying to solve?

 
21st February 2018


 


 
"But the theory was troubled. If you tried to compute it more accurately, you would find that the corrections you thought was going to be small (the next term in the series, for example) was in fact very large - in fact it was infinity!  So it turned out you couldn't really compute anything beyond a certain accuracy."

- Richard P. Feynman in QED: The Strange Theory of Light and Matter. 















"..But these changes in science are not made wantonly, but carefully and cautiously by the best minds and honest hearts, and not by any casual child who thinks that the world may be changed as easily as rolling off a log. "

- Lillian R. Lieber.
































 

    The idea behind Quantum Computing initially, was to explore the possibility of simulating physics using computers.  We were looking for exact solutions to the problems in physics.  In real life there were some really interesting problems which could not be solved using digital computers in reasonable time frame and without requiring excessive computational resources.  The applications for Quantum Computing being actively researched into, are encryption, reversible database search, machine learning etc.  Impressive stuff, except it does not give us a sense of why Quantum Computing should be considered a disruptive technology.

    For a technology to be qualified as a disruptive technology, it has to go into the mass production.  The invention of wheels and then their subsequent use in vehicles can be considered example of a disruptive technology from the early human history.  In modern world, personal computers and smart-phones represent examples of disruptive technologies.  So far we do not have any visibility on Quantum Computing approaching masses in near future.  It is likely to stay as a high priced computational device restricted to specialized domains.

    However the Quantum Computing is an extremely powerful concept, which if and when realized has the potential to transform the technological landscape.  Therefore it is a good exercise to understand what problems other than those known in physics and engineering, exist and need to be solved.  Whether these problems will be solved by the Quantum Computing or Topological Computing, we do not know yet.  These problems are independent of any specific knowledge domain and the path forward is obscure at best.  At a very high level, we can state the following:

"The problem to be solved, is to know or predict the outcome of the next instant, with absolute precision in the measurement space."

An observer who does not know this outcome, will not know what to do or where to be next.  As a consequence the observer will stay in the state of measurement.  If we recall this was the premise, based on which the concept of the discrete measurement space or j-space was developed.

    The prediction of the outcome of the next instant, is an extremely difficult business 1.  It can never be done in its entirety by a macroscopic observer.  However we have some respite in the sense that when we speak of a time-instant on the time-axis, we are effectively within a stable environment in the measurement metric of a macroscopic observer, which is based on the electron-photon interaction, as defined for the q = 3 space.  The information to be measured can be enormous from a macroscopic perspective, but it will always be finite. 

    Once we have moved into the q = 3 space, we have finite resources to complete the objective stated above 2.  Therefore the next level of the problem to be solved within human context, is the problem of the resource optimization 3.  The problem of resource optimization manifests itself in many ways in our daily lives.  More intelligent the solution, better the resource optimization and less is the waste.  Less waste means less entropy.  Therefore if we can achieve a zero-entropy solution within q = 3 state, we can perhaps solve the "impossible" problem. 

    Thus either Quantum or Topological Computer must provide the zero-entropy solution to a given problem.  Please note that a zero-entropy solution is equal to the single measurement (loge1 = 0) solution.  The zero-entropy solution brings us to the requirement of a universal computer capable of performing the reversible computing, as identified earlier.  The Quantum Computing in its current state, can not provide zero-entropy solutions.  That is why the Topological space and the concepts associated with it, become very important.

And then there is this small matter of finding the question, to which the answer is "42"....

______________
1. 
To know the outcome of the next instant, is "impossible" business.  If we already knew the outcome of the next instant, the measurements would not be needed to begin with.
2.  In physics we have an equivalent concept known as "action": the resources available in a conservative system, to travel a path AB; or equivalently the resources available in a conservative system, to measure all the information contained within the path AB.
3. The knowledge acquired in different specialized domains such as biology, physics, mathematics, philosophy etc., is the consequence of the solutions developed while an observer is trying to optimize resources in its environment.  Please note that an observer making measurements in j-space can be a biological cell, a molecule, a planet or a human being.  The objects being measured in j-space can be a biological cell, a molecule, a planet or a human being.  The equivalent of the "resource optimization" is finding the lowest energy state.  D-Wave's Quantum Annealer, is based on finding the lowest energy state for a given configuration.





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