QuantumCore

Hands-on lab · 1 step

Normalise a qubit state

Normalise (1+i)∣0⟩+2∣1⟩(1+i)\lvert0\rangle+2\lvert1\rangle and read off its Born probability P(1)P(1).

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Step 1: Normalise and measure

The vector ∣ψ~⟩=(1+i)∣0⟩+2∣1⟩\lvert\tilde\psi\rangle=(1+i)\lvert0\rangle+2\lvert1\rangle is not normalised. Enter the amplitudes α,β\alpha,\beta of ∣ψ⟩=∣ψ~⟩/∥ψ~∥\lvert\psi\rangle=\lvert\tilde\psi\rangle/\lVert\tilde\psi\rVert (as complex numbers) and the probability P(1)P(1) of outcome 11 in a ZZ measurement. Answers are accepted within 10−310^{-3}.

Enter exact expressions or decimals, e.g. 1/sqrt(2), pi/3, (1+i)/sqrt(6), exp(i*pi/4). Complex values are allowed.

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