[3PS]

Short answer, a qubit is a unit vector in a 2D complex Hilbert space. Now, that doesn't actually say much about why we care or how they're useful. In practical terms, you can think of qubits as complex unit vectors along two axes, with one axis corresponding to |0⟩ (the zero qubit) and one axis corresponding to |1⟩, or the one qubit. So for example, you could have a qubit called |+⟩, which is just shorthand for (|0⟩ + |1⟩)/sqrt(2).

Measuring a qubit in a basis collapses it to one of the basis vectors (e.g Schrödinger's cat must be alive or dead once we open the box) with probability equal to its inner product with that basis vector. This is why we need a Hilbert space and not just any old vector space.

Finally, to answer your question about gates, a quantum gate is basically a unitary matrix, i.e. a matrix that preserves the norm of its inputs. You can feed qubits into these matrices by themselves or, more often, many at once, by using something called the tensor product of the qubits - this is where the math gets slightly more involved.

The long and short of it is that we can induce correlation patterns between qubits using these gates (aka quantum entanglement) and orchestrate circuits of interference patterns where the wrong answers cancel each other out and the right answer gets reinforced so that we measure it at the end - unfortunately, this is where my knowledge breaks down as a beginner. My apologies if I accidentally handwaved anything important but hopefully you get the gist.

[tagrun]

This is like saying that voltage is a scalar real number, which explains nothing about the physics of electromagnetism, and in my opinion is probably the worst way to explain physics of anything. It especially tells nothing useful given the question is about the stuff that a qubit is made of (which is different from "how do you mathematically represent an ideal qubit on paper?").

And going beyond that, as Peres puts it, "Quantum phenomena do not occur in a Hilbert space. They occur in a laboratory."

[galaxyLogic]

> Schrödinger's cat must be alive or dead once we open the box

I recently had a conversation about this in another thread. It seems to me, and nobody tried to convince me otherwise, that the Cat would be the Observer. Therefore it would be dead, NOT dead AND alive, as soon as it observes the poisonous gas in its box.

[3PS]

So this is a little nuanced. It's true that quantum systems collapse on "observation", but that doesn't actually mean "observation by a sentient entity". It could really just be any interaction with the outside environment. (This is why qubits have to be kept incredibly well-isolated.) We don't really fully know exactly how this collapse works, and related speculation is generally classified under the measurement problem [1]. But it's true that one of the key points of Schrödinger when proposing his thought experiment was that the notion of measurement or observation was not fully defined under the Copenhagen interpretation.

Side note, it's not that the cat is observing poisonous gas, but rather, that a Geiger counter is set to detect whether a radioactive atom decays or not and triggers the release of some poisonous gas if so. So, classically, Schrödinger's cat would be either alive or dead 50% of the time, not 100% dead. There are plenty of alternative ways to reconcile this classical view with quantum mechanics. Perhaps the simplest and most well-known is the many-worlds interpretation [2], which states that both events occur, just in different timelines, and we don't know what timeline we ended up in until we open the box. (Of course, it is ridiculous to speculate as to which timeline "we" end up in before the experiment is carried out, because the people in both timelines would still be "us" - this can get awkward to think about.)

[1] https://en.wikipedia.org/wiki/Measurement_problem

[2] https://en.wikipedia.org/wiki/Many-worlds_interpretation

[tagrun]

That version of the though experiment is known as "quantum suicide": https://en.wikipedia.org/wiki/Quantum_suicide_and_immortalit...

[russdill]

The point of the thought experiment was to highlight the measurement problem in QM interpretations and the difficulty in defining the observer.

[empath75]

sure but that’s still all one quantum system from the perspective of any other observer outside of the box, including other cats.