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Quantum Fourier Transform

Quantum Fourier Transform is a quantum equivalent of the classical Fourier transform.

Like the classical Fourier transform, quantum Fourier transform (QFT) takes data from the original signal representation to the frequency domain representation. The QFT differs from the classical Fourier transform in that it operates on a superposition state and produces a different superposition state as the output. QFT works using interference, which as we saw in the first week makes the signal either stronger or weaker. The components interfere either constructively or destructively, depending on their amplitude and phase. Let’s take a look at a three-qubit example.


古典的なフーリエ変換と同様に、量子フーリエ変換(QFT)はデータ表現を元の信号から周波数領域に変換する操作を指します。 ですが、QFTは古典フーリエ変換と違い、重ね合わせの状態で動作し、出力となる別の重ね合わせを生成します。 QFTは、第一週で見てきたような波の干渉を利用し、波の位相及び振幅に応じて、信号を強め合ったり弱め合ったりします。 3量子ビットを使ったQFTの例を見てみましょう。

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Understanding Quantum Computers

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