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ntwalibas committed Nov 14, 2018
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Expand Up @@ -145,14 +145,14 @@ the quantum algorithm can work with. We can't use the flow in :numref:`classical
because it is not reversible. So we need to build an equivalent flow that has the same
effect but runnable on a quantum computer.

To make our oracles reversible, we use the following scheme, dubbed *XOR encoding of boolean functions*.
To make our oracles reversible, we use the following scheme, dubbing it *XOR encoding of boolean functions*.

.. admonition:: XOR encoding of boolean functions

Let :math:`f(x_1, x_2, \ldots, x_n):\mathbb{B}^n \to \mathbb{B}` be a boolean function.
Define :math:`F(x_1, x_2, \ldots, x_n, z):\mathbb{B}^{n+1} \to \mathbb{B}` as
Let :math:`f(x_1, x_2, \ldots, x_n):\mathbb{B}^n \to \mathbb{B}` be a boolean function.
| Define :math:`F(x_1, x_2, \ldots, x_n, z):\mathbb{B}^{n+1} \to \mathbb{B}` as
:math:`F(x_1, x_2, \ldots, x_n, z) = (x_1, x_2, \ldots, x_n, z \oplus f(x_1, x_2, \ldots, x_n))`.
The function :math:`F:\mathbb{B}^{n+1} \to \mathbb{B}` is an encoding of :math:`f:\mathbb{B}^n \to \mathbb{B}`.
| The function :math:`F:\mathbb{B}^{n+1} \to \mathbb{B}` is an encoding of :math:`f:\mathbb{B}^n \to \mathbb{B}`.

So we have transformed our classical function into a new function that is equivalent to it but with additional properties:
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