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katas/content/deutsch_algo/index.md

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@@ -142,15 +142,18 @@ Note that this algorithm requires only **1** oracle call, and always produces th
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We can follow the steps of the algorithm for the constant and the balanced scenarios using a neat visualization. Since Deutsch algorithm deals only with states with real amplitudes, we can map all states on the unit circle, and follow the state evolution through the steps.
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1-2. Start with a qubit in the $\ket{0}$ state and apply the $H$ gate to the qubit.
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1. Start with a qubit in the $\ket{0}$ state and apply the $H$ gate to the qubit.
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<br/>
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@[svg]({"path": "./media/Plus_state.svg"})
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3. Apply the oracle.
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2. Apply the oracle.
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Here, the difference between the two scenarios becomes noticeable. In the constant scenario, $\ket{0}$ and $\ket{1}$ states get the same phase (either $1$ or $-1$), so the state remains the same or acquires a global phase of $-1$, which is physically the same state. In the variable scenario, zero and one states get different phases, so the state changes!
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<br/>
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@[svg]({"path": "./media/Apply_oracle.svg"})
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4. Apply the $H$ gate to the qubit again.
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3. Apply the $H$ gate to the qubit again.
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Now, we get the $\ket{0}$ state for both constant scenarios and the $\ket{1}$ state for both variable scenarios!
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<br/>
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@[svg]({"path": "./media/Apply_hadamard.svg"})
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