Quantum Mechanics resonates well with me because it is the only science which has elements of the paranormal and mysticism embedded in it. To grasp it, one would have to adopt the mind of an iconoclast, and not only think in a queer way; but think in a way that is stranger than his/her native way of thinking.
The theory of quantum computing is especially mind-boggling, and furiously dizzying. Try to visualize in your mind 'parallel universes entangling to solve intractable problems'. It is hard - Isn't it?
Usually, if you posses an intuitive level of comprehension of quantum computing theory, you are either; mentally acute, and/or keenly imaginative, or just afflicted with a potent level of insanity (demented). I'd like to think that I fall into the keenly imaginative category, like the majority of the people who read Clive Staple Lewis' The Chronicles of Narnia in their juvenile years.
In the prequel of the series of The Chronicles of Narnia entitled The Magician's Nephew, Digory Kirke (the magician's nephew) and his new friend Polly Plummer enter into a 'portal land'/'central land'/'an in-between land', which has pools that lead to different worlds existing in parallel. Interestingly, the striking feature about all the lands they toggled back and forth from, is that they have unfathomably unique characteristics, and are abound with rich and endless adventures. Understandably, these are generally the flurry of images that are conjured up in the minds of most by the phrase parallel universes.
However, quantum computing, whilst riveting, is particularly bankrupt of the overflowing romance in The Chronicles of Narnia. Which begs the question of why the purveyors of quantum computing wisdom articulate the subject matter as if it were fantastical - like The Chronicles of Narnia. Their poor articulation of the subject matter, causes most people to misunderstand quantum computing; its capabilities; and, what it seeks to achieve.
From the outset, I must confess that I was one of the confused louts who misunderstood the florid phrase 'parallel universes entangling to solve intractable problems'. I comprehended it at a fantastical level (a.k.a as if it were The Chronicles of Narnia); instead of comprehending it at a more sedate realistic level. Obviously, I apportion most of the blame for my poor deconstruction of quantum computing theory, to poor articulation that is rife in many quantum computing research papers and articles. Another cause of this misinterpretation, albeit a minor one, is the keen imagination I nurture - which causes me to sometimes view things in a quixotic light. I only became clear about what the phrase truly meant, when I went through the quantum mathematics and quantum physics that underpins the theory of quantum computing.
In this post, I'll try to illuminate on what the pundits in the field of quantum computing mean by the phrase 'parallel universes entangling to solve computationally intractable problems'.
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Detailed explanation of the hypothetical graphical illustration: The illustration above shows the variability of the incomes of three groups of males over time; bankers, clerks and janitors. The horizontal axis represents time - incorporating all different flavors of the business cycle, and the vertical axis represents inflation adjusted income - meaning that all incomes under consideration are in 'constant dollar terms'. It is assumed in the illustration that income has a positive correlation to weight, height and I.Q. Thus, the adage underpinning this illustration is 'the higher the weight, height and I.Q. - the higher the income'. The sample of Bankers in this hypothetical case, has an average weight of 200lbs, is on average 6ft 1inch tall and has an intelligence quotient of 124 points. The sample of Clerks in this hypothetical case, has an average weight of 170lbs, is on average 5ft 11inches tall and has an intelligence quotient of 112 points. The sample of Janitors in this hypothetical case, has an average weight of 156lbs, is on average 5ft 6inches tall and has an intelligence quotient of 105 points. The Monte Carlo random run showing the cyclical variability of the incomes of Bankers is depicted by the navy-blue trajectory labeled A - which is the most turbulent; illustrating the high cyclical variability of a banker's income. In the illustration, the Monte Carlo random run showing the cyclical variability of the incomes of Clerks is depicted by the dark-green trajectory labeled B - which is more stable than A as evidenced by the smoother peaks and dips. Lastly, the Monte Carlo random run showing the cyclical variability of the incomes of Janitors is depicted by the lime-green trajectory labeled C - which is virtually flat, and is the most stable of all trajectories - indicating the 'cyclical-neutrality' of the incomes of janitors.
...Parallel Universes
The term 'universe' in statistics and logic simply means all objects a under consideration, or a population under consideration. In the graphical illustration in this post, there are three different discrete universes; A, B and C. Hence. it should be obvious now that in quantum computing jargon universe does not mean the cosmos, or all creation.
At time t1, the income of a banker is at1; a clerk is making bt1; and, a janitor is making ct1. Hence implying that at1 is parallel to bt1 and ct1 (at1 // bt1 // ct1), thereby implying that A is parallel to B and C (A // B // C). Therefore A, B and C are parallel universes. They are statistical observations related in that they explain different things happening at the same time to incomes of bankers, clerks and janitors. Not romantic like The Chronicles of Narnia at all!
...Entangling to Solve Intractable Problems
In the hypothetical graphical illustration above it is said that the vital statistics for bankers are: weight - 200lbs; height - 6ft 1 inch; I.Q. - 124. Clerks' statistics are: weight - 170lbs; height - 5ft 11 inches; I.Q. - 112. Janitors' statistics are: weight - 156lbs; height - 5ft 6 inches; I.Q. - 105.
Now, suppose that you are asked to map the cyclical variability (over time) of the income of a banker who weighs 200lbs, is 5ft 11 inches tall and has an I.Q. of 105 - a banker who's not represented by the universe labeled A: who has the weight of someone in the A universe; the height of someone in the B universe; and, the I.Q. of someone in the C universe. Someone who's the amalgam of specific individual characteristics of A, B, and C groups. What would you do?
I would average the each income observation of people in the A, B and C groups (i.e. [atx + btx+ ctx]/3) to derive each point of the trajectory illustrating the cyclical variability of the income of the atypical banker over time. However, that is a very crude way of solving the problem.
Height, Weight and I.Q., may not have an equal influence on income, and thus, I'd need to find the level of correlation between weight/I.Q./height and income, and factor that into my 'averaging',
A quantum computer can solve a more complex type of that problem (in the correct way) - with hundreds and thousands of universes, by taking each vital characteristic of each universe - taking into consideration the weighted impact the characteristic has on the point of interest; and blending it into the computational process to derive the end solution - at a frightening level of accuracy, and instantaneously. Hence the phrase parallel universes entangling to solve intractable problems.
Do you still think that quantum computing is romantic?
I don't.
Firstly, to understand the phrase 'parallel universes entangling to solve computationally intractable problems', it is important to de-construct the sentence into two key phrases, and to explain each phrase. Therefore, the key phrases in quote above are 'parallel universes' and 'entangling to solve computationally intractable problems'.
The hypothetical graphical illustration below will be used to explain both phrases:
The hypothetical graphical illustration below will be used to explain both phrases:
Detailed explanation of the hypothetical graphical illustration: The illustration above shows the variability of the incomes of three groups of males over time; bankers, clerks and janitors. The horizontal axis represents time - incorporating all different flavors of the business cycle, and the vertical axis represents inflation adjusted income - meaning that all incomes under consideration are in 'constant dollar terms'. It is assumed in the illustration that income has a positive correlation to weight, height and I.Q. Thus, the adage underpinning this illustration is 'the higher the weight, height and I.Q. - the higher the income'. The sample of Bankers in this hypothetical case, has an average weight of 200lbs, is on average 6ft 1inch tall and has an intelligence quotient of 124 points. The sample of Clerks in this hypothetical case, has an average weight of 170lbs, is on average 5ft 11inches tall and has an intelligence quotient of 112 points. The sample of Janitors in this hypothetical case, has an average weight of 156lbs, is on average 5ft 6inches tall and has an intelligence quotient of 105 points. The Monte Carlo random run showing the cyclical variability of the incomes of Bankers is depicted by the navy-blue trajectory labeled A - which is the most turbulent; illustrating the high cyclical variability of a banker's income. In the illustration, the Monte Carlo random run showing the cyclical variability of the incomes of Clerks is depicted by the dark-green trajectory labeled B - which is more stable than A as evidenced by the smoother peaks and dips. Lastly, the Monte Carlo random run showing the cyclical variability of the incomes of Janitors is depicted by the lime-green trajectory labeled C - which is virtually flat, and is the most stable of all trajectories - indicating the 'cyclical-neutrality' of the incomes of janitors....Parallel Universes
The term 'universe' in statistics and logic simply means all objects a under consideration, or a population under consideration. In the graphical illustration in this post, there are three different discrete universes; A, B and C. Hence. it should be obvious now that in quantum computing jargon universe does not mean the cosmos, or all creation.
At time t1, the income of a banker is at1; a clerk is making bt1; and, a janitor is making ct1. Hence implying that at1 is parallel to bt1 and ct1 (at1 // bt1 // ct1), thereby implying that A is parallel to B and C (A // B // C). Therefore A, B and C are parallel universes. They are statistical observations related in that they explain different things happening at the same time to incomes of bankers, clerks and janitors. Not romantic like The Chronicles of Narnia at all!
...Entangling to Solve Intractable Problems
In the hypothetical graphical illustration above it is said that the vital statistics for bankers are: weight - 200lbs; height - 6ft 1 inch; I.Q. - 124. Clerks' statistics are: weight - 170lbs; height - 5ft 11 inches; I.Q. - 112. Janitors' statistics are: weight - 156lbs; height - 5ft 6 inches; I.Q. - 105.
Now, suppose that you are asked to map the cyclical variability (over time) of the income of a banker who weighs 200lbs, is 5ft 11 inches tall and has an I.Q. of 105 - a banker who's not represented by the universe labeled A: who has the weight of someone in the A universe; the height of someone in the B universe; and, the I.Q. of someone in the C universe. Someone who's the amalgam of specific individual characteristics of A, B, and C groups. What would you do?
I would average the each income observation of people in the A, B and C groups (i.e. [atx + btx+ ctx]/3) to derive each point of the trajectory illustrating the cyclical variability of the income of the atypical banker over time. However, that is a very crude way of solving the problem.
Height, Weight and I.Q., may not have an equal influence on income, and thus, I'd need to find the level of correlation between weight/I.Q./height and income, and factor that into my 'averaging',
A quantum computer can solve a more complex type of that problem (in the correct way) - with hundreds and thousands of universes, by taking each vital characteristic of each universe - taking into consideration the weighted impact the characteristic has on the point of interest; and blending it into the computational process to derive the end solution - at a frightening level of accuracy, and instantaneously. Hence the phrase parallel universes entangling to solve intractable problems.
Do you still think that quantum computing is romantic?
I don't.
