blue_239k是能工智人喵喵喵

Contest 1

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A1 Generate State $\ket{+}$

The Plus state is defined as

$$\ket{+}=\frac{1}{\sqrt{2}}(\ket{0}+\ket{1})$$

Global phase ignored.

Sol:

Apply Hadamard gate $H$ to (0).

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A2 Generate Uniform Superposition State

The uniform superposition state $\ket{A}$ is defined as

$$\ket{A}=\frac{1}{\sqrt{2^n}}\sum_{i=0}^{2^n-1}\ket{i}_n$$

$1\le n\le 10$

Global phase ignored.

Sol:

Apply Hadamard gate $H$ to (0) to (n-1) .

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A3 Generate state $\frac{1}{\sqrt{2}}(\ket{0}+\ket{3})$

The state $\ket{\psi}$ is defined as

$$\ket{\psi}=\frac{1}{\sqrt{2}}(\ket{0}+\ket{3})=\frac{1}{\sqrt{2}}(\ket{00}+\ket{11})$$

Global phase ignored.

Sol:

Apply Hadamard gate $H$ to (0).

Apply Controlled-Not gate $CX$ to (0,1).

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A4 A5 Generate state $\frac{1}{\sqrt{3}}(\ket{0}+\ket{1}+\ket{2})$

The state $\ket{\psi}$ is defined as

$$\ket{\psi}=\frac{1}{\sqrt{3}}(\ket{0}+\ket{1}+\ket{2})=\frac{1}{\sqrt{3}}(\ket{00}+\ket{10}+\ket{01})$$

Global phase ignored.

Sol:

Let $\theta=2\arcsin(\frac{1}{\sqrt{3}})$.

Apply Rotate-Y gate $RY$ to ($\theta$,1).

Apply Not gate $X$ to (1).

Apply Controlled-Rotate-Y gate $CRY$ to ($\frac{\pi}{2}$,1,0).

Apply Not gate $X$ to (1).