I think this deserves more emphasis: regardless of whether or not we need a quantum computer in the end, as a model quantum computing is apparently useful to do research with and advance the status quo of our knowledge.
The abstract does too: https://arxiv.org/abs/1807.04271
When we realize that ‘quantum’ computing is really just ‘analog’, we’ll see a resurgence in that too.
(Which is great actually, because modern analog computers are stunningly capable. And yes, they are the same thing when you realize that the hardware is exactly the same, and sampling away the noise has the same form as solving for decoherence.)
> And yes, they are the same thing when you realize that the hardware is exactly the same
Quantum computers don't actually exist yet. It's a theoretical model. There's no hardware.
Even for the theoretical models, we have plenty of alternative models. The circuit model is the de-facto standard and a good thought framework, but there are real concerns about it maybe not to being the model to translate into actual hardware. (analogously, lambda calculus vs RTL) It will be interesting to see what alternative or new theoretical models pop up once the quantum computer's equivalent of the transistor surfaces.
Another thought to consider is since our computation latencies are currently restricted by sampling (clock) times, which is restricted by power (for heating reasons which are predicted by quantum), would the smarter bet be to pursue technology which uses exponentially less energy (analog) or technology which uses exponentially more energy with the same promised speed ups as the former (quantum)?
Analog computers in their ideal form (known as real computers after the real numbers) are also strictly superior to classical computers. But unlike quantum computers, we know for sure that ideal analog computers can not exist. This also follows from QM. (Intuitively, real numbers don't exist in physics and everything ultimately becomes quantized)
Given your same line of reasoning, we are able to measure real numbers, in fact you can derive discrete numbers from real numbers while the converse is not true. Intuitively, discrete numbers don't exist and everything ultimately becomes real numbers. This is obviously a correct following of the stimulating rhetoric yet completely untrue. The ability of derivation from an axiom has nothing to do with the validity of the derivative representations.
† https://www.eetimes.com/document.asp?doc_id=1138111 †† https://ieeexplore.ieee.org/document/7463004/
> we are able to measure real numbers
I disagree with you here. I like to believe in the Church-Turing-Deutsch thesis, which implies that reality is ultimately discrete and real numbers are nonphysical. The example you give, time, is indeed a real number in our best models of physics. But this is mostly because we don't know how to quantize it yet. It's one of the biggest open problems in physics. That said, the outcome could indeed be that it is a real number and CTD is wrong.
That metaphor seems to confuse people more than it clarifies. Did you perhaps mean "nature's programming language"?
It would be fun if quantum computing were equivalent to classical (less fun -- probabilistic) models with comparable complexity, just more intuitive. I guess lots of complexity conjectures can be phrased that way, though -- P vs NP for sure.
If so, I'd say,
- It didn't really seem like anyone in the comment thread was trying to make a "compelling" argument for anything -- we're just chatting here.
- If we were interested in that sort of thing, we might note that minimal program size is a good measure of language complexity/information, and that "algorithms from the book" and different models of computation that might make programs easier to write are both "objectively interesting" from an information-theoretic standpoint.
EDIT: oh wait, I get it, you weren't being constructive, you just came here to make fun of a religion nobody was talking about. Never mind.
The law of gravity is a different kind of thing to a rock. It is not a physical object, it describes the ways physical objects behave. The number 3 is a different kind of thing to 3 apples. It is not a physical-natural object, it describes aspects of nature.
Its the difference between the rules of chess and the board and pieces. Both are essential parts of the game 'chess' but we can usefully distinguish them when we want to be more precise.
There is no controversy here.
This is probably because religions have traditionally framed extra-universal things as ordering events inside the universe, but it seems that is not possible if you exit spacetime.
In other words, branes, strings, gods, or anything we discover could, in my definition, "cause" reality to manifest without a temporal cause/effect coupling.
Perhaps I need a better word to remove the cause/effect temporal baggage
In terms of proof, we also don't know whether reason can be applied to things within nature -- it's still depending on axioms. But we still believe it to be true and to be applicable everywhere inside nature regardless of specific context, and I see no reason (pun intended) not to extend this belief even outside nature.
There is the set A. It contains all elements except itself.
There is a subset of A called P, which is all possible things.
There is a subset of P called M, which is all things that manifest in reality.
Traditionally we call elements of M "things that exist (or did exist or will exist)"
You're saying that P=M?
I find that position extraordinary and lacking evidence.
If there's infinite matter arranged randomly then you would expect to eventually find one of everything finite.
We can say things that aren't disagreements. We can even disagree without controversy.
You seem to be having a knee-jerk reaction to the word "God". Your personal preference for the most secular language possible is not a valid reason to pick apart GP's phrasing.
> First, he was wrong
I agree. And that's completely and totally irrelevant. I have no idea why you even mention it. Obviously what matters is that his meaning is clear.
> Second, he said that in a very different culture. This isn't the 1920s.
So your objection to GP's phrasing, in spite of it being completely inoffensive and having a perfectly clear meaning, is "because it's $CURRENT_YEAR".
QM without collapse is actually a fully deterministic theory. And it makes sense that the universe doesn’t play dice - because there is no source of randomness available.
It’s a functional language.
> there is no source of randomness available
I think that's going beyond what we can be sure of. We have no evidence that there is randomness, be we also have no evidence that there isn't.
QM may be fully deterministic if we disregard collapse, but as far as I'm aware, we can't do that. Collapse is still something we have to contend with given the current state of our knowledge.
I suppose we can't rule out collapse totally, but we also can't rule out fairies pushing atoms around. It's just that there is no evidence for collapse, so it seems we can ignore it.
It takes one bit of information to specify that a coin is tails-up, regardless of whether it was placed that way deliberately or got that way as a result of a random coin toss.
For example if you know you're in a universe where coins always land tail up then you need 0 bits to store that state.
Of course you could make a similar claim about a universe where coin flips always alternate--current state is merely a function of time and initial conditions, and therefore no information is needed to store it. But then you're saying that deterministic universes contain no information at all except their initial state. That's fine, but I personally wouldn't put an axiom like that on the winning side of Occam's razor.
How can it be otherwise? You can always completely describe the deterministic universe by its initial state plus a time value, even if its initial state appears much simpler than the later states.
A busy game of life scenario can arise from a simple starting point. If you don't know the rules, you're stuck describing the position of every dot, if you do, then you can create a complete description with much less information.
By which one?
> randomness - it always comes from somewhere
Unless randomness is a fundamental property of matter.
> can't rule out fairies pushing atoms around
Wasn't it exactly what the Bell's experiments disproved?
The date that he said isn't relevant either -- nor the culture at that date, since it doesn't affect whether this is "confusing" or not, and I don't see anything drastically different in our culture to render it so. (Or even to render a reference to God "offensive" or a bad metaphor today, if that was your argument)
It can change state arbitrarily, introspect all the data and step forward in execution.
It works in the comparison that quantum computing often sensationalized by media.
That it applies to physics too is expected, because one way to characterise the quantum language is that it defines what one system can possibly do or say to another system.
The source of those limitations is not yet completely clear, i.e. it hasn't been satisfactorily axiomized. But we can get close and it seems it's a logical restraint based around self-consistency. Assuming the universe must be self-consistent, it must also obey QM.
Also, with natural units Plank's constant is 2π, so it does show up a lot.