Call me a cantankerous old fart but I continue to find the quantum computing wars to be a singular encapsulation of the Breathtaking Stupidity of Our Age. There are endless papers proving statements about computation in the physical world.
While the assembled idiot authors are supremely confident in their respective proofs, they have not the wit to get down to actually building anything. Instead we are stuck with what I call: Church-Turing Noise. This involves people making assertions about what can or cannot be done in the Real World based on mathematical reasoning alone.
There is a rather elementary difficulty with all this contemporary noise and nonsense.
One cannot actually prove a property of the physical world through mathematical manipulations. It was not so long ago, as little as thirty years, that scientists, mathematicians and (yes) high--school teachers understood this fact.
It is central to the empirical nature of scientific knowledge.
Certainly, we can make postulates about the world. Definitely, we can axiomatize those into a series of abstractions with which to reason about the world. However, we cannot prove properties of Nature by cogitation alone. That path leads to Perdition...
However, the Road to Perdition is the path that contemporary Physics has taken - we are now deep into the Dark Age of Modern Physics. It is a terrible thing to witness, and poses a grave risk to human progress. I despair of finding common sense in this realm.
All cogent evidence of incompleteness in the quantum mechanical axioms has simply been ignored. Theories founded on different tenets which make acceptable contact with experiment have also been ignored. The fiction of certainty is substituted.
In place of educated questioning doubt, we now have uneducated voluble certainty.
Result: an Entire Generation of Non-Scientists busy proving the Nature of Reality.
They will, indeed they must, prove the Nature of Reality by cogitation alone!
There is no room for humble doubt that the ultimate axioms are unknown. NO. We are now certain we know the quantum rules. In that case, why bother with experiment? Why even build a quantum computer? How wondorous the achievement of our time!
We are quantum teleported straight back into the Dark Ages of Ignorance.
These are the Marks of Mediocrity, the dark foetid depths to which Science has sunk.
This was precisely the error of Greek Philosophers and something which took a genius of the stature of Galileo to dispel. In one fell swoop, this giant of human history torpedoed the Ptolemaic System. His direct observation of the Moons of Jupiter shattered the conception of Crystal Spheres, as dramatized so well in Bertolt Brecht's play The Life of Galileo:
GALILEO Now we have proof. The fourth must have moved behind Jupiter where we can't see it. There you have a star with another revolving around it.
SAGREDO But the crystal sphere that Jupiter is fastened to?
GALILEO Where is it indeed? How can Jupiter be fastened to anything if other stars revolve around it? There is no scaffolding in the sky, there's nothing holding the universe up! There you have another sun!
SAGREDO Calm down. You're thinking too fast.
GALILEO Fast, hell! Man, get excited! You're seeing something that nobody ever saw before. They were right!
SAGREDO Who? The Copernicans?
GALILEO Yes, and you know who. The whole world was against them, and yet they were right.
Here we have the story of all scientific progress in a nutshell.
The prior belief, born of the Ptolemaic system, is the notion of a geocentric system with the planets and sun orbiting the earth. These were supported by crystal spheres.
Of course, in the dramatization of Brecht, Galileo and Sagredo are in discussion about the obvious inconsistency caused by the observations of moons about Jupiter. How could that be, if Jupiter was anchored to such a sphere? Surely they (the moons in orbit) would Shatter the Crystal Sphere. Whether factual or not, the point is well-dramatized. Inconsistent theories simply point the way to better theories.
Galileo was right: Fast, hell! Man, get excited about the Discovery of Quantum Incompleteness! You are seeing something that nobody ever saw before.
The connection between this piece of history and today is the continuing infatuation with quantum computation. Many otherwise thoughtful persons are caught in the grip of this psychological tractor beam. Quantum computing is special. Quantum computing is different. Quantum computing is Wondrous. The blather never ceases...
Certainly, computation on a quantum substrate will be different in many ways and not a little special and/or interesting. It will have serious commercial applications.
However, one can prove, in strong form, an elementary property of the mathematical systems employed in this crazy Church-Turing conversation.
As I showed more than fifteen years prior, in my Adelaide Festschrift article: The Schrödinger equation from three postulates it is possible to fully embed quantum dynamics inside classical dynamics.
(here is the PDF)
Let me try to explain what that means in practical terms for the benefit of the over-excited quantum computing types.
The mathematics of classical mechanics fully contains quantum mechanics as a special case. Here, as in much of the English language, special emphatically means less general.
In strictly provable mathematical sense, it is a specialization. For complexity theory zealots, that means any quantum computer can be fully simulated by a classical computer. Ohh... bummer. There goes the delusion of grandeur.
That is a genuine provable statement in the mathematical world. It is the reason why the present crop of theorem wielding wet-behind-the-ears complexity theorists can be very safely boxed about the ears and told to: 1) firstly, shut-up; 2) go away and learn some mathematics; and 3) come back when you understand what Science is actually about.
Of course, the astute reader will immediately respond:
How can you criticize people for using mathematical proofs to say something about the real world when you yourself use a mathematical proof to say something strong and didactic about the nascent field of quantum computing?
That is a very valid question. It is because I am using a mathematical proof to assert something about a mathematical system.
I am simply saying that, in a strictly provable sense, quantum computers (as a class) are less general and can be completely simulated by classical computers. We are not talking about what you can and cannot do in Nature. Indeed, that is a more open question.
Logically, and provably, this means that most of the discussion is about nothing. Folks are excitedly proving all the wonderful things that could be done by a quantum computer that could also be done by a classical computer.
Importantly, the classical computer in the above scenario is more general than the quantum computer. Put differently, the classical computer could do some things the quantum computer could not. One of those things is to simulate dynamical chaos.
You would think, would you not, that with all these mega-geniuses running around in quantum computing that they would know this?
Well, apparently not.
Perhaps they cannot read? Perhaps they cannot think? Perhaps they do not want to?
Who knows? Who cares? It is the Dark Age of Science, don't you know?
Just make it all up and then go Make Some Noise.
How absurd the delusions of our time.