Those probability distributions are typically represented as complex vectors and quantum gates as unitary matrix operations on those vectors. Here's a quantum

Those probability distributions are typically represented as complex vectors and quantum gates as unitary matrix operations on those vectors. Here's a quantum computer simulator [1] I wrote years ago that allows you to construct quantum circuits using the most common quantum gates found in literature. This is all done by the application of complex matrices. On the right there is the probability distribution that taking a measurement would result in. [1] https://github.com/qcsimulator/qcsimulator.github.io https://github.com/qcsimulator/qcsimulator.github.io Edit: It's worth noting that we can study quantum computing without a quantum computer, just as we can study computing without a classical computer. Edit 2: Here's Grover's Algorithm in my simulator where you can see that the probability of measuring the correct "hidden" oracle value is 96% after only three applications of the diffusion operator: https://qcsimulator.github.io/?example=Grover%27s%20Algorithm https://qcsimulator.github.io/?example=Grover%27s%20Algorith...