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I'm a bit familiar with the concept of stochastic computing, where numbers are stored in large bit streams called "Stochastic Numbers", which represent numbers in the domain $[0,1]$ typically.
The Wikipedia article on stochastic computing summarizes all basic concepts and history behind it.
Does any of the concepts of stochastic computing relate to quantum computing? Or are they two very different ways of treating calculations?
Scott Aaronson relates quantum and stochastic computation as follows: quantum computation is stochastic computation, but using the 2-norm instead of the 1-norm as the conserved quantity.
In both paradigms you form vectors of weighted states, and operate on those vectors using matrices. So they have many similarities. But in stochastic computation the weights have to add up to 1 (as probabilities do) whereas for quantum computation the squares of the weights have to add up to 1 (as amplitudes do).
The two are very different ways of treating calculations. You've probably heard that qbits "can be both 0 and 1 at the same time" or similar; this isn't accomplished by assigning them a value in the domain $[0, 1]$, but rather a linear combination of $0$ and $1$:
$\alpha|0\rangle + \beta|1\rangle = \begin{bmatrix} \alpha \\ \beta \end{bmatrix}$
This is called a state vector, and quantum operations take the form of matrices multiplying this state vector.
If you're interested in learning more, I have created a video on quantum computing you might find instructive here.
