QuantumCore

Hands-on lab · 1 step

Exponentiate a Pauli generator

Use X2=IX^2=I to sum the power series of e−iαXe^{-i\alpha X} in closed form and write the matrix of RX(π/3)=e−i(π/3)X/2R_X(\pi/3)=e^{-i(\pi/3)X/2}.

0/1 step passedBest score 0/100

Step 1: The rotation R_X(π/3)

Let X=(0110)X=\begin{pmatrix}0&1\\1&0\end{pmatrix} and θ=π/3\theta=\pi/3. Enter the 2×22\times2 complex matrix of e−iθX/2e^{-i\theta X/2} in the computational basis, with rows and columns ordered ∣0⟩,∣1⟩\lvert0\rangle,\lvert1\rangle. The check is phase-sensitive: a global phase eiγUe^{i\gamma}U with γ≠0\gamma\neq0 is a different matrix and is marked wrong. Entries are accepted within 10−310^{-3}.

Enter each entry as an expression, e.g. 1/sqrt(2), -i/2, exp(i*pi/4). Rows run top to bottom, columns left to right.

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Fill every entry with a valid expression.