QCC 2022, Home Work 3
1. A circuite for the Quantum Discrete Fourier Transform (QDFT) with N = 4 (n = 2 qubits) is shown below. Let
|v1⟩ = |10⟩ and |v2⟩ = |11⟩
be used at the input of this circuite and |w1⟩ and |w2⟩ be the states at
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the output of the circuite. Find |w1⟩ and |w2⟩.
Figure 1: Quantum DFT, n = 2.
2. A circuite for the inverse QDFT is shown below. Let the input states be |w1⟩ and |w2⟩ obtained in the previous problem. Let |u1⟩ and |u2⟩ be the output states. Find |u1⟩ and |u2⟩.
Figure 2: Quantum Inverse DFT, n = 2. Reminding: S† denotes the Hermitian conjugation of S.
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