Uh... one of those algorithms in your list is literally for speeding up linear algebra. Do you think just because it sounds technical it's "businessy"? All modern technology is technical, that's what technology is. It would be like someone saying, "GPUs would be useless to regular people because all they mainly do is speed up matrix multiplication. Who cares about that except for businesses?" Many of these algorithms here offer potential speedup for linear algebra operations. That is the basis of both graphics and AI. One of those algorithms is even for machine learning in that list. There are various algorithms for potentially speeding up matrix multiplication in the linear. It's huge for regular consumers... assuming the technology could ever progress to come to regular consumers.

Classical computers compute using 0s and 1s which refer to something physical like voltage levels of 0v or 3.3v respectively. Quantum computers also compute using 0s and 1s that also refers to something physical, like the spin of an electron which can only be up or down. Although these qubits differ because with a classical bit, there is just one thing to "look at" (called "observables") if you want to know its value. If I want to know the voltage level is 0 or 1 I can just take out my multimeter and check. There is just one single observable.

With a qubit, there are actually three observables: σ~x~, σ~y~, and σ~z~. You can think of a qubit like a sphere where you can measure it along its x, y, or z axis. These often correspond in real life to real rotations, for example, you can measure electron spin using something called Stern-Gerlach apparatus and you can measure a different axis by physically rotating the whole apparatus.

How can a single 0 or 1 be associated with three different observables? Well, the qubit can only have a single 0 or 1 at a time, so, let's say, you measure its value on the z-axis, so you measure σ~z~, and you get 0 or 1, then the qubit ceases to have values for σ~x~ or σ~y~. They just don't exist anymore. If you then go measure, let's say, σ~x~, then you will get something entirely random, and then the value for σ~z~ will cease to exist. So it can only hold one bit of information at a time, but measuring it on a different axis will "interfere" with that information.

It's thus not possible to actually know the values for all the different observables because only one exists at a time, but you can also use them in logic gates where one depends on an axis with no value. For example, if you measure a qubit on the σ~z~ axis, you can then pass it through a logic gate where it will flip a second qubit or not flip it because on whether or not σ~x~ is 0 or 1. Of course, if you measured σ~z~, then σ~x~ has no value, so you can't say whether or not it will flip the other qubit, but you can say that they would be correlated with one another (if σ~x~ is 0 then it will not flip it, if it is 1 then it will, and thus they are related to one another). This is basically what entanglement is.

Because you cannot know the outcome when you have certain interactions like this, you can only model the system probabilistically based on the information you do know, and because measuring qubits on one axis erases its value on all others, then some information you know about the system can interfere with (cancel out) other information you know about it. Waves also can interfere with each other, and so oddly enough, it turns out you can model how your predictions of the system evolve over the computation using a wave function which then can be used to derive a probability distribution of the results.

What is even more interesting is that if you have a system like this where you have to model it using a wave function, it turns out it can in principle execute certain algorithms exponentially faster than classical computers. So they are definitely nowhere near the same as classical computers. Their complexity scales up exponentially when trying to simulate quantum computers on a classical computer. Every additional qubit doubles the complexity, and thus it becomes really difficult to even simulate small numbers of qubits. I built my own simulator in C and it uses 45 gigabytes of RAM to simulate just 16. I think the world record is literally only like 56.

I feel like there is a pretty big gap between understanding how logic gates and truth tables work and understanding the underlying physics of how modern processors work.

Yes, the problem with quantum mechanics is it's not just your Deepak Chopras of the world that get sucked into quantum woo, but even a lot of respectable academics with serious credentials, thus giving credence to these ideas. Quantum mechanics is a context-dependent theory, the properties of systems are context variant. It is not observer-dependent. The observer just occupies their own unique context and since it is context-dependent, they have to describe things from their own context.

It is kind of like velocity in Galilean relativity, you have to take into account reference frame. Two observers in Galilean relativity could disagree on certain things, such as the velocity of an object but the disagreement is not "confusing" because if you understand relativity, you'd know it's just a difference in reference frame. Nothing important about "observers" here.

I do not understand what is with so many academics in fully understanding that properties of systems can be variant under different reference frames in special relativity, but when it comes to quantum mechanics their heads explode trying to interpret the contextual nature of it and resort to silly claims like saying it proves some fundamental role for the conscious observer. All it shows is that the properties of systems are context variant. There is nothing else.

Once you accept that, then everything else follows. All of the unintuitive aspects of quantum mechanics disappear, you do not need to posit systems in two places at once, some special role for observers, a multiverse, nonlocality, hidden variables, nothing. All the "paradoxes" disappear if you just accept the context variance of the states of systems.

You shouldn't take it that seriously. MWI has a lot of zealots in the popular media who act like it's a proven fact, kind of like some String Theorists do, but it is actually rather dubious.

MWI claims it is simpler because they are getting rid of the Born rule, so it has less assumptions, but the reason there is the Born rule in QM is because... well, it's needed to actually predict the right results. You can't just throw it out. It's also impossible to derive the Born rule without some sort of additional assumption, and there is no agreed upon way to do this.[1]

This makes MWI actually more complicated than traditional quantum mechanics because they have to add different arbitrary assumptions and then add an additional layer of mathematics to derive the Born rule from it, rather than assuming it. These derivations also tend to be incredibly arbitrary because the assumptions you have to make to derive it are always chosen specifically for the purpose of deriving the Born rule and don't seem to make much sense otherwise, and thus are just as arbitrary as assuming the Born rule directly.[2] [3]

If you prefer a video, the one below discusses various "multiverse" ideas including MWI and also discusses how it ultimately ends up being more mathematically complicated than other interpretations of QM.

https://www.youtube.com/watch?v=QHa1vbwVaNU

MWI also makes no sense for a separate reason. If you consider the electromagnetic field for example, how do we know it exists? We know it exists because we can see its effect on particles. If you drop some iron filings around a magnet, it conforms to the shape of a field, but ultimately what you are seeing is the iron filings and not the field itself, but the effects of the field. Now, imagine if someone claimed the iron filings don't even exist, only the field. You'd be a bit confused because, well, you only know the field exists because of its effects on the filings. You can't see the field, only the particles, so if you deny the particles, then you're just left in confusion.

This is effectively what MWI does. We live in a world composed of spacetime containing particles, yet wave functions describe, well, waves made of nothing that exist in an abstract space known as Hilbert space. Schrodinger's derivation of his famous wave equation is based on observing the behavior of particles. MWI denies particles even exist and everything is just waves in Hilbert space made of nothing, which is very bizarre because then you would be effectively claiming the entire universe is composed of something entirely invisible. So how does that explain everything we see?

[I]t does not account, per se, for the phenomenological reality that we actually observe. In order to describe the phenomena that we observe, other mathematical elements are needed besides ψ: the individual variables, like X and P, that we use to describe the world. The Many Worlds interpretation does not explain them clearly. It is not enough to know the ψ wave and Schrödinger’s equation in order to define and use quantum theory: we need to specify an algebra of observables, otherwise we cannot calculate anything and there is no relation with the phenomena of our experience. The role of this algebra of observables, which is extremely clear in other interpretations, is not at all clear in the Many Worlds interpretation.

--- Carlo Rovelli, Helgoland: Making Sense of the Quantum Revolution

The philosopher Tim Maudlin has a whole lecture you can watch below on this problem, pointing out how MWI makes no sense because nothing in the interpretation includes anything we can actually observe. It quite literally describes a whole universe without observables.

https://www.youtube.com/watch?v=us7gbWWPUsA

Not to rain on your parade or anything if you are just having fun, but there is a lot of misinformation on websites like YouTube painting MWI as more reasonable than it actually is, so I just want people to be aware.

Physicists seem to love their confusing language. Why do they associate Bell's theorem with "local realism"? I get "local," that maps to Lorentz invariance. But what does "realism" even mean? That's a philosophical term, not a physical one, and I've seen at least 4 different ways it has been defined in the literature. Some papers use the philosophical meaning, belief in an observer-independent reality, some associate it with the outcome of experiments being predictable/predetermined, some associate it with particles having definite values at all times, and others argue that realism has to be broken up into different "kinds" of realism like "strong" realism and "weak" realism with different meanings.

I saw a physicist recently who made a video complaining about how frustrated they are that everyone associates the term "dark matter" with matter that doesn't interact with the electromagnetic field (hence "dark"), when in reality dark matter just refers to a list of observations which particle theories are currently the leading explanation for but technically the term doesn't imply a particular class of theories and thus is not a claim that the observations are explained by matter that is "dark." They were like genuinely upset and had an hour long video about people keep misunderstanding the term "dark matter" is just a list of observation, but like, why call it dark matter then if that's not what it is?

There really needs to be some sort of like organization that sets official names for terminology, kinda like how the French government has an official organization that defines what is considered real French so if there is any confusion in the language you at least have something to refer to. That way there can be some thought put into terminology used.

We can't see wave functions. It is a tool used to predict observations but itself cannot be observed, and cannot be an observable object as it exists in an abstract Hilbert space and not even in spacetime. It is only "space" in the sense of a state space, kind of like how if I have a radio with 4 knobs, I can describe the settings with a single point in a 4 dimensional space. That doesn't mean the radio actually is a 4 dimensional object existing in this state space, it only means that we can represent that way for convenience, and the dimensions here moreso represent degrees of freedom.

If you believe everything is a wave function then you believe the whole universe is made out of things that cannot be observed. So how does that explain what we observe? Just leads to confusion. Confusion not caused by the mathematics but self-imposed. Nothing about the mathematics says you literally have to think everything is made out of waves. In fact, Heisenberg's original formulation of quantum mechanics made all the same predictions yet this was before the Schrodinger equation was even invented.

People take the wave formulation way too literally and ultimately it just produces much of this confusion. They are misleadingly taught that you can think of things turning into waves by starting with the double-slit experiment, except it is horribly misleading because they think the interference pattern they're seeing is the wave function. Yet, (1) the wave function is associated with individual particles, not the interference pattern which is formed by thousands, millions of particles. There is nothing wave-like visible with just a single particle experiment. (2) Even the interference pattern formed by millions of particles does not contain the information of the wave function, only a projection of it, sort of like its "shadow" as the imaginary terms are lost when you apply the Born rule to it and square it. (3) They also like to depict a literal wave moving through two slits, but again there are imaginary components which don't map to anything physically real, and so the depiction is a lie as information has to be removed in order to actually display a wave on the screen.

The moment you look at literally anything that isn't the double-slit experiment, the intuitive notion of imagining waves moving through space breaks down. Consider a quantum computer where the qubits are electrons with up or down spin representing 0 or 1. You can also represent the state of the quantum computer with a wave function, yet what does it even mean to imagine the computer's internal state is a wave when there is nothing moving at all and the state of the quantum computer doesn't even have position as one of its values? You can't point to that wave even existing anywhere, you get lost in confusion if you try.

This cloud is described by a mathematical object called wave function. The Austrian physicist Erwin Schrödinger has written an equation describing its evolution in time. Quantum mechanics is often mistakenly identified with this equation. Schrödinger had hopes that the ‘wave’ could be used to explain the oddities of quantum theory: from those of the sea to electromagnetic ones, waves are something we understand well. Even today, some physicists try to understand quantum mechanics by thinking that reality is the Schrödinger wave. But Heisenberg and Dirac understood at once that this would not do.

To view Schrödinger’s wave as something real is to give it too much weight – it doesn’t help us to understand the theory; on the contrary, it leads to greater confusion. Except for special cases, the Schrödinger wave is not in physical space, and this divests it of all its intuitive character. But the main reason why Schrödinger’s wave is a bad image of reality is the fact that, when a particle collides with something else, it is always at a point: it is never spread out in space like a wave. If we conceive an electron as a wave, we get in trouble explaining how this wave instantly concentrates to a point at each collision. Schrödinger’s wave is not a useful representation of reality: it is an aid to calculation which permits us to predict with some degree of precision where the electron will reappear. The reality of the electron is not a wave: it is how it manifests itself in interactions

Carlo Rovelli, "Reality is Not What it Seems"

It is more intuitive to not think of wave functions as entities at all. But people have this very specific mathematical notation so burned into their heads from the repeated uses of the double-slit experiment that it is very difficult to get it out of their heads. Not only did Heisenberg instead use matrix transformation rather than the Schrodinger equation to represent QM, but it is also possible to represent quantum mechanics in even a third mathematical formulation known as the ensemble in phase space formulation.

The point here is that the Schrodinger equation is just one mathematical formalism in which there are multiple mathematically equivalent ways to formulate quantum mechanics, and so treating these wave functions wave really existing waves moving through a Hilbert space which you try to imagine as something like our own spacetime seems to be putting too much weight on a very specific formalism and ultimately is the source of a lot of the confusion. Describing the whole universe as thus a giant wave in Hilbert space evolving according to the Schrodinger equation is thus rather dubious, especially since these are entirely metaphysical constructs without any observable properties.

I agree experience is incalculable but not because it is some special immaterial substance but because experience just is objective reality from a particular context frame. I can do all the calculations I want on a piece of paper describing the properties of fire, but the paper it's written on won't suddenly burst into flames. A description of an object will never converge into a real object, and by no means will descriptions of reality ever become reality itself. The notion that experience is incalculable is just uninteresting. Of course, we can say the same about the wave function. We use it as a tool to predict where we will see real particles. You also cannot compute the real particles from the wave function either because it's not a real entity but a description of relationships between observations (i.e. experiences) of real things.

There 100% are…

If you choose to believe so, like I said I don't really care. Is a quantum computer conscious? I think it's a bit irrelevant whether or not they exist. I will concede they do for the sake of discussion.

Penrose thinks they’re responsible for consciousness.

Yeah, and as I said, Penrose was wrong, not because the measurement problem isn't the cause for consciousness, but that there is no measurement problem nor a "hard problem." Penrose plays on the same logical fallacies I pointed out to come to believe there are two problems where none actually exist and then, because both problems originate from the same logical fallacies. He then notices they are similar and thinks "solving" one is necessary for "solving" the other, when neither problems actually existed in the first place.

Because we also don’t know what makes anesthesia stop consciousness. And anesthesia stops consciousness and stops the quantum process.

You'd need to define what you mean more specifically about "consciousness" and "quantum process." We don't remember things that occur when we're under anesthesia, so are we saying memory is consciousness?

Now, the math isn’t clean. I forget which way it leans, but I think it’s that consciousness kicks out a little before the quantum action is fully inhibited? It’s been a minute, and this shit isn’t simple.

Sure, it's not simple, because the notion of "consciousness" as used in philosophy is a very vague and slippery word with hundreds of different meanings depending on the context, and this makes it seem "mysterious" as its meaning is slippery and can change from context to context, making it difficult to pin down what is even being talked about.

Yet, if you pin it down, if you are actually specific about what you mean, then you don't run into any confusion. The "hard problem of consciousness" is not even a "problem" as a "problem" implies you want to solve it, and most philosophers who advocate for it like David Chalmers, well, advocate for it. They spend their whole career arguing in favor of its existence and then using it as a basis for their own dualistic philosophy. It is thus a hard axiom of consciousness and not a hard problem. I simply disagree with the axioms.

Penrose is an odd case because he accepts the axioms and then carries that same thinking into QM where the same contradiction re-emerges but actually thinks it is somehow solvable. What is a "measurement" if not an "observation," and what is an "observation" if not an "experience"? The same "measurement problem" is just a reflection of the very same "hard problem" about the supposed "phenomenality" of experience and the explanatory gap between what we actually experience and what supposedly exists beyond it.

It’s the quantum wave function collapse that’s important.

Why should I believe there is a physical collapse? This requires you to, again, posit that there physically exists something that lies beyond all possibilities of us ever observing it (paralleling Kant's "noumenon") which suddenly transforms itself into something we can actually observe the moment we try to look at it (paralleling Kant's "phenomenon"). This clearly introduces an explanatory gap as to how this process occurs, which is the basis of the measurement problem in the first place.

There is no reason to posit a physical "collapse" or even that there exists at all a realm of waves floating about in Hilbert space. These are unnecessary metaphysical assumptions that are purely philosophical and contribute nothing but confusion to an understanding of the mathematics of the theory. Again, just like Chalmers' so-called "hard problem," Penrose is inventing a problem to solve which we have no reason to believe is even a problem in the first place: nothing about quantum theory demands that you believe particles really turn into invisible waves in Hilbert space when you aren't looking at them and suddenly turn back into visible particles in spacetime when you do look at them.

That's entirely metaphysical and arbitrary to believe in.

There’s no spinning out where multiple things happen, there is only one thing. After wave collapse, is when you look in the box and see if the cats dead. In a sense it’s the literal “observer effect” happening our head. And that is probably what consciousness is.

There is only an "observer effect" if you believe the cat literally did turn into a wave and you perturbed that wave by looking at it and caused it to "collapse" like a house of cards. What did the cat see in its perspective? How did it feel for the cat to turn into a wave? The whole point of Schrodinger's cat thought experiment was that Schrodinger was trying to argue against believing particles really turn into waves because then you'd have to believe unreasonable things like cats turning into waves.

All of this is entirely metaphysical, there is no observations that can confirm this interpretation. You can only justify the claim that cats literally turn into waves when you don't look at them and there is a physical collapse of that wave when you do look at them on purely philosophical grounds. It is not demanded by the theory at all. You choose to believe it purely on philosophical grounds which then leads you to think there is some "problem" with the theory that needs to be "solved," but it is purely metaphysical.

There is no actual contradiction between theory and evidence/observation, only contradiction between people's metaphysical assumptions that they refuse to question for some reason and what they a priori think the theory should be, rather than just rethinking their assumptions.

That’s how science works. Most won’t know who Penrose is till he’s dead.

I'd hardly consider what Penrose is doing to be "science" at all. All these physical "theories of consciousness" that purport not to just be explaining intelligence or self-awareness or things like that, but more specifically claim to be solving Chalmers' hard axiom of consciousness (that humans possess some immaterial invisible substance that is somehow attached to the brain but is not the brain itself), are all pseudoscience, because they are beginning with an unreasonable axiom which we have no scientific reason at all to take seriously and then trying to use science to "solve" it.

It is no different then claiming to use science to try and answer the question as to why humans have souls. Any "scientific" approach you use to try and answer that question is inherently pseudoscience because the axiomatic premise itself is flawed: it would be trying to solve a problem it never established is even a problem to be solved in the first place.

Roger Penrose is pretty much the only dude looking into consciousness from the perspective of a physicist

I would recommend reading the philosophers Jocelyn Benoist and Francois-Igor Pris who argue very convincingly that both the "hard problem of consciousness" and the "measurement problem" stem from the same logical fallacies of conflating subjectivity (or sometimes called phenomenality) with contextuality, and that both disappear when you make this distinction, and so neither are actually problems for physics to solve but are caused by fallacious reasoning in some of our a priori assumptions about the properties of reality.

Benoist's book Toward a Contextual Realism and Pris' book Contextual Realism and Quantum Mechanics both cover this really well. They are based in late Wittgensteinian philosophy, so maybe reading Saul Kripke's Wittgenstein on Rules and Private Language is a good primer.

That’s the only way free will could exist...What would give humans free will would be the inherent randomness if the whole “quantum bubble collapse” was a fundamental part of consciousness.

Even if they discover quantum phenomena in the brain, all that would show is our brain is like a quantum computer. But nobody would argue quantum computers have free will, do they? People often like to conflate the determinism/free will debate with the debate over Laplacian determinism specifically, which should not be conflated, as randomness clearly has nothing to do with the question of free will.

If the state forced everyone into a job for life the moment they turned 18, but they chose that job using a quantum random number generator, would it be "free"? Obviously not. But we can also look at it in the reverse sense. If there was a God that knew every decision you were going to make, would that negate free will? Not necessarily. Just because something knows your decision ahead of time doesn't necessarily mean you did not make that decision yourself.

The determinism/free will debate is ultimately about whether or not human decisions are reducible to the laws of physics or not. Even if there is quantum phenomena in the brain that plays a real role in decision making, our decisions would still be reducible to the laws of physics and thus determined by them. Quantum mechanics is still deterministic in the nomological sense of the word, meaning, determinism according to the laws of physics. It is just not deterministic in the absolute Laplacian sense of the word that says you can predict the future with certainty if you knew all properties of all systems in the present.

If the conditions are exactly the same down to an atomic level… You’ll get the same results every time

I think a distinction should be made between Laplacian determinism and fatalism (not sure if there's a better word for the latter category). The difference here is that both claim there is only one future, but only the former claims the future is perfectly predictable from the states of things at present. So fatalism is less strict: even in quantum mechanics that is random, there is a single outcome that is "fated to be," but you could never predict it ahead of time.

Unless you ascribe to the Many Worlds Interpretation, I think you kind of have to accept a fatalistic position in regards to quantum mechanics, mainly due not to quantum mechanics itself but special relativity. In special relativity, different observers see time passing at different rates. You can thus build a time machine that can take you into the future just by traveling really fast, near the speed of light, then turning around and coming back home.

The only way for this to even be possible for there to be different reference frames that see time pass differently is if the future already, in some sense, pre-exists. This is sometimes known as the "block universe" which suggests that the future, present, and past are all equally "real" in some sense. For the future to be real, then, there has to be an outcome of each of the quantum random events already "decided" so to speak. Quantum mechanics is nomologically deterministic in the sense that it does describe nature as reducible to the laws of physics, but not deterministic in the Laplacian sense that you can predict the future with certainty knowing even in principle. It is more comparable to fatalism, that there is a single outcome fated to be (that is, again, unless you ascribe to MWI), but it's impossible to know ahead of time.

My issue it is similar: each "layer" of simulation would necessarily be far simpler than than the layer in which the simulation is built, and so complexity would drop down exponentially such that even an incredibly complex universe would not be able to support conscious beings in simulations within only a few layers. You could imagine that maybe the initial universe is so much more complex than our own that it could support millions of layers, but at that point you're just guessing, as we have no reason to believe there is even a single layer above our own, and the whole notion that "we're more likely to be an a simulation than not" just ceases to be true. You can't actually put a number on it, or even a vague description like "more likely." it's ultimately a guess.

I have never understood the argument that QM is evidence for a simulation because the universe is using less resources or something like that by not "rendering" things at that low of a level. The problem is that, yes, it's probabilistic, but it is not merely probabilistic. We have probability in classical mechanics already like when dealing with gasses in statistical mechanics and we can model that just fine. Modeling wave functions is far more computationally expensive because they do not even exist in traditional spacetime but in an abstract Hilbert space that can grows in complexity exponentially faster than classical systems. That's the whole reason for building quantum computers, it's so much more computationally expensive to simulate this that it is more efficient just to have a machine that can do it. The laws of physics at a fundamental level get far more complex and far more computationally expensive, and not the reverse.