The Impossibilities Of Quantum Computing

Since we’ll soon be discussing cause in the Class, and nowhere is cause as difficult as it is in quantum mechanics, and because somebody recently reminded me of Scott Locklin’s lovely rant against the idea of quantum computing, I thought I’d use the subject as an excuse to explain why quantum computing has stalled. (Physics has also gone off into other preposterousities, like Many Worlds (blog/Substack).)

Let’s start with “The Case Against Quantum Computing” by Mikhail Dyakonov (Locklin cites this). I urge you to read it all, since I will only pull a limited summary.

Ordinary transistors are On or Off, and can be engineered well enough for you to read these words. Qubits (which I’m assuming you’ve heard of) are modeled on a wave function on things that can take, when measured, one of two states. The model is just that: a model. The states when measured are also just that: measured.

Dyakonov uses as an example electron spin, which can be up or down when measured. When modeled, the probability of it being measured up or down relies on a function of two complex numbers. These numbers are on the continuum, meaning, in the model, they have an uncountable infinite number of possible values. Hence the probabilities are also on the continuum.

Recall the size of the infinity of the continuum is infinitely larger than the simple counting infinity, which is already infinite (blog/Substack). It’s big. Strange thing about infinity and human thinking is we can never really imagine it other than a large number that we can get close to. Which we cannot. Any effort we make will always be infinitely far from the goal. This limitation is the source of much misery, as we’ll see in time.

What about Reality? Some say (in popular accounts) the electron is simultaneously both spin up and spin down. This is absurd, as Dyakonov highlights.

Yes, quantum mechanics often defies intuition. But this concept shouldn’t be couched in such perplexing language. Instead, think of a vector positioned in the x-y plane and canted at 45 degrees to the x-axis. Somebody might say that this vector simultaneously points in both the x- and y-directions. That statement is true in some sense, but it’s not really a useful description. Describing a qubit as being simultaneously in both [UP] and [DOWN] states is, in my view, similarly unhelpful. And yet, it’s become almost de rigueur for journalists to describe it as such. [I can’t get the arrow html to stick, so put in up and down.]

That vector is a wonderful analogy, and it can be carried much further. About that, more another day.

One modeled qubit requires, in theory, tracking two infinitely valued numbers. Two requires four (two for each). For 1,000 gates, which is not many, it requires (Dyakonov does the math) tracking about 10^300 infinitely valued numbers. How many is that? “It is much, much greater than the number of subatomic particles in the observable universe…A useful quantum computer needs to process a set of continuous parameters that is larger than the number of subatomic particles in the observable universe” (his emphasis).

All this is before error correction, which only swells the requirements to greater impossibilities. And I mean that last word strictly.

In the math, the continuity of the numbers is what gives them their charm, and allows all the theoretical solutions that are eagerly anticipated, like factoring large numbers (to defeat certain cryptographic schemes). In the objects which become actual qubits, however, there isn’t an actual infinity of anything. The model says there is, but that’s the model. In Reality, no. This reminds us of the infamous model of Zeno’s paradox of parts.

From Ed Feser’s Aristotle’s Revenge (p 17; a book that is mandatory reading):

Zeno reinforced Parmenides’ line of argument with his paradox of parts. Suppose there are distinct things in the world. Then, Zeno says, they would have to have some size or other, and of course, common sense takes things to have different sizes. But anything having size can be divided into parts of smaller size, and these parts can in turn be divided into yet smaller parts, ad infinitum. Hence things having size will have an infinite number of parts. But since something is larger the more parts it has, something with an infinite number of parts will be infinitely large. Hence if there are distinct things in the world they will all be of infinite size, and for that reason will all be the same size. But those conclusions are, need- less to say, absurd. Hence the assumption that led us to these absurdities, namely the assumption that there are distinct things in the world, must be false.

The solution is that all these subdivisions are only there potentially, not actually, and that only some are actually there. Because Reality has it that objects are part potential and part actual, both aspects of being. This is the classic Aristotelian philosophy that even Heisenberg tried reminding his colleagues of—to little success. So far.

But we’ll see it in practice, in the quantum computers that are built, and not just in theory. Real qubits won’t behave according to the model, though they may appear to up to a point. And that point is our ability to measure and our finite abilities to build. Don’t forget that no matter much scientists brag that their QM models have been confirmed to the n-th digit, they are still an infinite distance away from confirming them absolutely.

Qubits in practice can’t behave in an infinite fashion, because, even supposing the complex numbers representing objects are real, objects cannot actually take an infinite number of values. In Reality, most values will only be there potentially and never actually.

Dyakonov reminds us (as I am constantly doing) of how our actual measurements on real objects can only be finite—and discrete, at that. “Tuning” transistors to On and Off is easy. But anybody who has tried, say, tuning two IF stages for a peak, or build a reflective optic—whose values in theory are also infinite—knows that perfection is not possible. How could this be done for 10^300 such objects, at a minimum, in constant flux? It cannot.

Not that something cannot come out of these constructions. But the grandiose advertising claims for quantum computers (“all solutions are there at once!”) won’t hold in practice. Not because our engineering isn’t good enough. Because it will never be. There is no way to build or measure anything to infinite precision. Real electronics (or optics or whatever) don’t or can’t hold actual infinities of states.

What’s lacking is a proper philosophy of nature, the ground on which physics itself rests. We’ll be covering the replacement, which I only hinted at above (and of course did not justify here). But I’d bet that once it is replaced, quantum computers can be seen more soberly. Real advances can be made. But that means discovering why these values are actual, and why that infinite leftover are not. I don’t know how to do this. But maybe you can figure it out.

I’ll have suggestions on how to do that in the Class.

More cold water poured on QCs: “Quantum Computing’s Hard, Cold Reality Check“.

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