QuantumCore

Hands-on lab · 1 step

Build a rank-one projector

Write the matrix of P=∣+i⟩⟨+i∣P=\lvert{+i}\rangle\langle{+i}\rvert using (∣a⟩⟨b∣)jk=ajbk‾(\lvert a\rangle\langle b\rvert)_{jk}=a_j\overline{b_k}.

0/1 step passedBest score 0/100

Step 1: Outer product of |+i⟩

Let ∣+i⟩=12(∣0⟩+i∣1⟩)\lvert{+i}\rangle=\tfrac1{\sqrt2}(\lvert0\rangle+i\lvert1\rangle). Enter the 2×22\times2 complex matrix of the projector P=∣+i⟩⟨+i∣P=\lvert{+i}\rangle\langle{+i}\rvert in the computational basis, with rows and columns ordered ∣0⟩,∣1⟩\lvert0\rangle,\lvert1\rangle. 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.