It is only continuous because it is random, so prior to making a measurement, you describe it in terms of a probability distribution called the state vector. The bits 0 and 1 are discrete, but if I said it was random and asked you to describe it, you would assign it a probability between 0 and 1, and thus it suddenly becomes continuous. (Although, in quantum mechanics, probability amplitudes are complex-valued.) The continuous nature of it is really something epistemic and not ontological. We only observe qubits as either 0 or 1, with discrete values, never anything in between the two.

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.

Even if you believe there really exists a “hard problem of consciousness,” even Chalmers admits such a thing would have to be fundamentally unobservable and indistinguishable from something that does not have it (see his p-zombie argument), so it could never be something discovered by the sciences, or something discovered at all. Believing there is something immaterial about consciousness inherently requires an a priori assumption and cannot be something derived from a posteriori observational evidence.

We feel conscious and have an internal experience

It does not make sense to add the qualifier “internal” unless it is being contrasted with “external.” It makes no sense to say “I’m inside this house” unless you’re contrasting it with “as opposed to outside the house.” Speaking of “internal experience” is a bit odd in my view because it implies there is such thing as an “external experience”. What would that even be?

What about the p-zombie, the human person who just doesn’t have an internal experience and just had a set of rules, but acts like every other human?

The p-zombie argument doesn’t make sense as you can only conceive of things that are remixes of what you’ve seen before. I have never seen a pink elephant but I’ve seen pink things and I’ve seen elephants so I can remix them in my mind and imagine it. But if you ask me to imagine an elephant a color I’ve never seen before? I just can’t do it, I wouldn’t even know what that means. Indeed, a person blind since birth cannot “see” at all, not in their imagination, not even in their dreams.

The p-zombie argument asks us to conceive of two people that are not observably different in every way yet still different because one is lacking some property that the other has. But if you’re claiming you can conceive of this, I just don’t believe you. You’re probably playing some mental tricks on yourself to make you think you can conceive of it but you cannot. If there is nothing observably different about them then there is nothing conceivably different about them either.

What about a cat, who apparently has a less complex internal experience, but seems to act like we’d expect if it has something like that? What about a tick, or a louse? What about a water bear? A tree? A paramecium? A bacteria? A computer program?

This is what Thomas Nagel and David Chalmers ask and then settles on “mammals only” because they have an unjustified mammalian bias. Like I said, there is no “internal” experience, there is just experience. Nagel and Chalmers both rely on an unjustified premise that “point-of-view” is unique to mammalian brains because supposedly objective reality is point-of-view independent and since experience clearly has an aspect of point-of-view then that means experience too must be a product purely of mammalian brains, and then demands the “physicalists” prove how non-experiential reality gives rise to the experiential realm.

But the entire premise is arbitrary and wrong. Objective reality is not point-of-view independent. In general relativity, reality literally change depending on your point-of-view. Time passes a bit faster for people standing up than people sitting down, lengths of rulers can change between observers, velocity of objects can change as well. Relational quantum mechanics goes even further and shows that all variable properties of particles depend upon point-of-view.

The idea that objective reality is point-of-view independent is just entirely false. It is point-of-view dependent all the way down. Experience is just objective reality as it actually exists independent of the observer but dependent upon the point-of-view in which they occupy. It has nothing to do with mammalian brains, “consciousness,” or subjectivity. If reality is point-of-view dependent all the way down, then it is not even possible to conceive of an intelligent being that would occupy a unique point-of-view, because everything occupies their own unique point-of-view, even a rock. It’s not a byproduct of the “conscious mind” but just a property of objective reality: experience is objective reality independent of the observer, but dependent upon the context of that experience.

There’s a continuum one could construct that includes all those things and ranks them by how similar their behaviors are to ours, and calls the things close to us conscious and the things farther away not, but the line is ever going to be fuzzy. There’s no categorical difference that separates one end of the spectrum from the other, it’s just about picking where to put the line.

When you go down this continuum what gradually disappears is cognition, that is to say, the ability to think about, reflect upon, be self-aware of, one’s point-of-view. The point-of-viewness of reality, or more simply the contextual nature of reality, does not disappear at any point. Only the ability to talk about it disappears. A rock cannot tell you anything about what it’s like to be a rock from its context, it has no ability to reflect upon the point-of-view it occupies.

Although you’re right there is no hard-and-fast line for cognition, but that’s true of anything in nature. There’s no hard-and-fast line for anything. Take a cat for example, where does the cat begin and end, both in space in time? Create a rigorous definition of its borders. You won’t be able to do it. All our conceptions are human creations and therefore a bit fuzzy. Reality is infinitely complex and we cannot deal with the infinite complexity all at once so we break it up into chunks that are easier to work with: cats, dogs, trees, red, blue, hydrogen, helium, etc. But you always find when you look at these things a little more closely that their nature as discrete “things” becomes rather fuzzy and disappears.

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.