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We have 4 numbers x = [x1, x2, x3, x4]

We want to prepare quantum state Psi somehow to encode x

We want to make QFT on Psi to get Phi = QFT (Psi)

Steve Bermeo
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1 Answers1

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For QFT, the numbers on which the transform is applied are encoded as amplitudes of the basis states: |x⟩ = ∑ xₖ |k⟩.

In your case you'd use a 2-qubit state and use amplitudes x₀ ... x₃, normalized. Then you'd prepare a state x₀ |00⟩ + x₁ |10⟩ + x₂ |01⟩ + x₃ |10⟩ (assuming little-endian encoding of the basis states). If you're implementing this using some quantum programming language, there's likely to be a library to do that for you - for example, in Q# it's PrepareArbitraryState.

Mariia Mykhailova
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  • This is part of a set up, so that I can then apply the Quantum Fourier Transform. I have to figure it out via pen and paper before I code it. Thanks for the answer, it's steering me in the right direction – Steve Bermeo Aug 04 '20 at 15:53