A qubit state is a simple, finite version of the wavefunction used in general quantum mechanics.
Understanding this connection lets you move from the circuit language of qubits to the wider subject of quantum mechanics without feeling like you are learning a completely different theory. The same rules apply -- just with a bigger state space.
For a particle moving in space, the quantum state is written as a wavefunction. It plays the same role as the qubit state, but instead of just two amplitudes (for 0 and 1), it has an amplitude for every possible position. You get the probability of finding the particle at a given position by squaring the wavefunction there. Phase still matters -- it determines how the wavefunction interferes with itself over time.
A qubit is like a menu with two items. A wavefunction is the same idea with an enormous menu -- one amplitude for each possible position. The rules are the same (amplitudes combine, then you square to get probabilities), but the menu is much larger.
The wavefunction (x,t) is a complex-valued function. Its squared magnitude |(x,t)|² gives a probability density for position: the probability of finding the particle between x and x+dx is |(x,t)|² dx. Like qubit amplitudes, the wavefunction carries phase information that affects how it evolves and interferes.
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