A plausible explanation of decoherence in quantum systems

Quantum computing pundits and entrepreneurs have, thus far, failed to bring into being a robust quantum computing system that can solve NP-complete problems.

The key/main stumbling block in their path is the inexplicable onset of decoherence in the quantum computing systems they fashion to solve intractable problems.

To describe decoherence succinctly: Quantum data (which is measured in qubits) is extremely volatile/fragile, and it easily vaporizes, or dissipates into its environment during a computational process, before any decipherable output is produced (which results in the output of incomplete and incorrect results). This is known as decoherence in the field of quantum computing.

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I was hunting for the possible causes of decoherence, and I think that I found a plausible cause of the phenomenon in a theory propounded by Messrs. John Conway and Simon Kochen, which they coined The Free Will Theorem.

The gist of the Conway-Kochen Free Will Theorem (which is, by the way, thoroughly enthralling) is this: Messrs. Conway and Kochen say they have proved that if human beings have free will, then elementary particles—like atoms, photons and electrons—possess free will as well.

Applied within the context of quantum computing: If we postulate that The Free Will Theorem holds, and if we assume that human beings have free will, then we can deduce that atoms, photons and electrons also have free will. Hence, this implies that decoherence in quantum computing systems is caused by atoms, photons and electrons that exercise their power of free will and choose not to be harnessed to manipulate data.

Kind of spooky isn't it?

Will D-Wave Systems Produce A Robust Quantum Computer?

In a prior post entitled Emergence of 'Super-Quant' Funds, I enunciated that D-Wave Systems, a precocious Canadian start-up, is currently at an advanced stage of creating a cutting-edge processor that uses a computational model known as adiabatic quantum computing (AQC), to solve complex search and optimization problems. If everything progresses smoothly, D-Wave Systems-created quantum computing solutions should be commercially available in the foreseeable future.

Underpinning the tremendous computational puissance of D-Wave Systems' computing solutions, is a processor that is fabricated using a super-conducting metal called niobium. When chilled to near absolute-zero temperatures, specifically when it is chilled to a temperature of 9.2 Kelvin, niobium loses all its electrical resistance and starts to behave like matter at its most rudimentary level, i.e quantum mechanically. Hence, this super-conducting property of niobium allows D-Wave Systems to fashion 'normal-sized' circuits, using currently-existing lithography technology, that operate using the principles of quantum mechanics (when chilled to ~9.2 Kelvin), i.e. they behave like 'circuits of atoms'.

This all resonated well with me until I encountered Sir Roger Penrose's Interpretation (The Penrose Interpretation) about the mass-scale at which standard quantum mechanics will fail. According to a Wikipedia Entry:

• "Penrose's idea is a variant of objective collapse theory. In these theories the wavefunction is a physical wave, which undergoes wave function collapse as a random process, with observers playing no special role. Penrose suggests that the threshold for wave function collapse is when superpositions involve at least a Planck mass worth of matter. He then hypothesizes that some fundamental gravitational event occurs, causing the wavefunction to choose one branch of reality over another. The exact way in which this choice happens he doesn't specify in any mathematically precise way.

  Accepting that wavefunctions are physically real, Penrose believes that things can exist in more than one place at one time. In his view, a macroscopic system, like a human being, cannot exist in more than one position because it has a significant gravitational field. A microscopic system, like an electron, has an insignificant gravitational field, and can exist in more than one location almost indefinitely."

Hence, this implies that any system above the Planck Mass, which is ~1e-8kg (According to Suzanne Gildert), fails to maintain coherence for any measurable amount time, due to the onset of gravitational interactions. Thus, this means that the mass of a system has a bearing, or an impact, on its ability to maintain quantum coherence.

According to Suzanne Gildert, one molecule of a niobium contains ~ 6e23 conduction electrons which have a mass of ~ 5e-7 kg. Since 5e-7 kg > 1e-8kg, any macro system fashioned from niobium may fail to maintain quantum coherence because of the onset of gravitational interactions. Hence the question (which is the title of this post): Will D-Wave Systems Produce A Robust Quantum Computer?

In my opinion: The D-Wave Systems' quantum computing solution has better chances of maintaining quantum coherence (being robust) in a zero-gravity chamber!

Quantum Computing: Parallel Universes (Revisited)

Every denizen of this planet has encountered this phrase at least once: "Your life is the partial expression/partial product of the choices you made from the time you were conceived up to this present moment". Conversely, it also holds that: "Your life is the partial expression/partial product of the choices you didn't make from the time you were conceived up to this present moment".

...This may seem like an astute play of words, but this example will illuminate on what I mean:

On a planet located in a distant galaxy that is 124 light-years from the Milky Way, there are only two distinct species of intelligent beings: Zoogles and Boogles. Zoogles are different to Boogles and, in fact they can be regarded as extreme opposites. Zoogles don't commingle with other Zoogles, and Boogles don't commingle with other Boogles. The inhabitants of this weird planet hang out in pairs (a Boogle and a Zoogle), with their perfect opposites. Hence, this means that any being you encounter on that weird celestial body is either a Zoogle or a Boogle. Which, therefore, implies that a Boogle is any randomly selected intelligent being on the planet who is not a Zoogle, and vice-versa.

Let us postulate that the distant planet is the multiverse, or grand universe of the totality of choices you could ever make, and couldn't/didn't make in your life, and that the universe, or subset illustrating the choices you actually managed to make is represented by the Boogles, and that the choices you didn't or couldn't make are represented by Zoogles. If someone knew every single Zoogle on this planet, and knew their individual character traits, he/she could work out the individual character traits of all Boogles, without even meeting a single Boogle (remember: Boogles are the extreme opposites of Zoogles), but then he'd/she'd be still left with the task of appending the character traits he/she arrives at, to individual Boogles. If he/she had additional information on Boogles and Zoogles that associated which each other, the task of appending the character traits he/she arrives at, to individual Boogles becomes easier. Therefore, the example simply serves to illustrate how an object can be abstractly constructed, when information on the particular object is lacking, from information on its perfect opposite. Hence you can see why it is also true that: "Your life is the partial expression/partial product of the choices you didn't make from the time you were conceived up to this present moment."

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More on choices: Everyone has a specific choice they made, that changed the course of the rest of their lives. For Bill Gates, his life-changing choice was to create software called BASIC for the MITS Altair 8800 - which, in essence, laid the foundations for Microsoft: a company that made him a billionaire.

If Bill Gates hadn't decided to create software for the MITS Altair 8800, what course would his life have taken? Would his life be like what is right now?

Of course it wouldn't, it would have taken a totally different course. That is in essence, what the term 'parallel universes' in quantum computing seeks to describe - different future 'realities' that a particular organism would find itself immersed in--or different realities it would experience--because of minor variations in the organism's present and past environmental circumstances (that may/may not be partially shaped by the choices the particular organism makes). These different realities are as infinite as the choices an organism makes during its lifetime, and are termed parallel universes in quantum computing terminology.

Makes sense now?

Quantum Computing: Parallel Universes

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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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:

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.