Need Help in Understanding expval() in class MeasureAll

#1

Hi Quantum People,

I have a question about the expval() function that is used in the class MeasureAll. The line of code that I don’t understand is shown in the following figure.

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Let’s ignore the batch size. So, probs is a vector [p0, p1] where p0 is the marginal probability of 0 and p1 is the marginal probability of 1. And observable.eigenvals is [1, -1] for PauliZ. Thus, res = [p0, p1] * [1, -1] = p0 - p1.

Question: what is the math meaning of doing probs.mv(observable.eigvals)? And what is the physical meaning?

Thanks for your time,
Caitao Zhan

#2

My question is resolved. It is the formula for calculating the expectation value of the Pauli Z operator. It is a measure of how much the probabilities are biased toward |0> and |1>.

|psi> = alpha |0> + beta |1>
<Z> = |alpha|^2 - |beta|^2

For more, see this wonderful lecture on Youtube from NYU Quantum:
hi