Quantum Fourier Transform

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The quantum Fourier transform (QFT) function is the quantum analog for discrete Fourier transform. It is applied on the quantum register state vector.

The state vector x is transformed to y in the following manner:

\[y_{k} = \frac{1}{\sqrt{N}} \sum_{j=0}^{N-1} x_j e^{2\pi i \frac{jk}{N}}\]

Function: qft

Arguments:

• target: QArray[QBit]

The target quantum argument is the quantum state on which we apply the QFT.

Example

from classiq import Output, QArray, QBit, allocate, create_model, qft, qfunc


@qfunc
def main(x: Output[QArray[QBit]]):

    allocate(4, x)
    qft(x)


qmod = create_model(main)

from classiq import synthesize, write_qmod

write_qmod(qmod, "qft")
qprog = synthesize(qmod)