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In describing quantum computers page in the fourth quick quiz it asks "An n-qubit state vector can contain up to $2^n$ amplitudes. What’s the largest number of transition amplitudes we’d need to represent any quantum operation on n qubits?"

My question is why is $4^n$ is wrong and $(2^n)^2$ is right, when $4^n = (2^n)^2$? Or is my math just wrong? I tried $n=1,...,5$. Isn't $(2^n)^2 = 2^{n\cdot 2} = 2^{2n} = (2^2)^n = 4^n$?

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Yes, both these answers should work.

My guess is, the quiz author was looking for alternative answers that looked similar to the correct one but were incorrect, and accidentally got a second correct one instead. If there is a way to provide feedback on that page, you can try letting the authors know - I know I'm always happy when someone catches a bug that I didn't!

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  • $\begingroup$ I didn't see a way to provide feedback. I was directed to this forum so I hope the author reads this. $\endgroup$
    – Tony
    Dec 22 '21 at 21:45
  • $\begingroup$ @Tony please create an issue on Github page of the Qiskit Texbook: github.com/qiskit-community/qiskit-textbook/issues $\endgroup$
    – 3yakuya
    Dec 29 '21 at 23:12

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