Representing a Marginal Probability
Explore how to represent marginal probabilities on a single qubit using quantum gates such as Hadamard and RY. Understand the process of converting probabilities to angles for parameterized quantum circuits, allowing precise control over measurement outcomes in quantum machine learning tasks.
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We start with letting a qubit represent the marginal probability of one event. A marginal probability is the absolute probability of the event irrespective of any further information. If we have multiple states where the event occurs, then the marginal probability is the sum of all the corresponding probabilities.
In the figure with one Hadamard-gate, there’s only one state where qubit 0 is 1. Therefore, the marginal probability is 0.5. In the figure with four Hadamard gates, there are eight states where qubit 0 is 1. The marginal probability of qubit 0 being 1 is the sum of all these states’ probabilities. It is 0.5, too.
The Hadamard-gate splits the overall probability into equal halves, but a marginal probability can be any value between 0.0 and 1.0.
In the lesson Gamble with Quantum Computing, we introduced the ...