QHack 2023: 4 week prep challenge, day 11, A Quantum Adder (QFT)

Today, I’m continuing with the next exercise from the algorithms track. The task is to build a number adder using the Fourier space.

Firstly, a Fourier transform is applied on the initial state, i.e. a state |0> or |1> in the computational basis is flipped into the X-Y-plane. The qubits are then rotated around the Z-axis, with an angle according to the number to add. Eventually, the state is transformed back from the Fourier space.

The transformation rule for the QFT reads

\[ QFT|x\rangle = \frac{1}{\sqrt{M}} \sum^{M-1}_{k=0} \exp(\frac{2 \pi i}{M} x k) |k\rangle \]

If you now want to add to a state in the Fourier space, you have to rotate the qubits accordingly. It is important to notice, that a rotation only effects the |1> portion, but not the |0> portion of a qubit’s state.

Having that in mind, it was relatively straight forward to come up with the solution…

def qfunc_adder(m, wires):
    """Quantum function capable of adding m units to a basic state given as input.

    Args:
        - m (int): units to add.
        - wires (list(int)): list of wires in which the function will be executed on.
    """

    qml.QFT(wires=wires)

    for w, _ in enumerate(wires):
        angle = m*np.pi/(2**w)
        qml.RZ(angle, wires=w)

    qml.QFT(wires=wires).inv()

… the tests check out, success!

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