0
$\begingroup$

I'm having trouble unifying these two ideas. When I read examples using, say, qiskit, it's typical to measure a qubit, so that to find the probability of measuring a state $|\psi \rangle$ in the state $|x\rangle$ is $p(|x \rangle) = (\langle x | \psi \rangle)^2$.

But when I read quantum computing textbooks, they usually refer to some observable that is getting measured. So what is the operator that gets measured when we "measure a qubit"? Is it the identity operator or something?

$\endgroup$
1

1 Answer 1

2
$\begingroup$

"Measure qubit $q$" = "Measure the $Z_q$ operator"

More generally, "measure the operator $P$" can be operationalized as "apply a sequence operations which sends $P \rightarrow Z_q$ then measure qubit $q$ then undo the operations to restore $Z_q \rightarrow P$.

$\endgroup$
2
  • $\begingroup$ What exactly is the $Z_q$ operator? The Pauli $Z$ matrix? $\endgroup$
    – theQman
    Aug 17, 2022 at 18:07
  • $\begingroup$ Exactly, measuring a qubit implicitly means measuring the Pauli-$Z$ observable on the $q$th qubit. This is because $Z$ is already diagonal in the computational basis. $\endgroup$
    – Cody Wang
    Aug 17, 2022 at 19:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.