1.4.2 Making your own operations

So far, we only know how to create the $[0]$ and $[1]$ states using Quirky. To create an interesting probability distribution, we can use the reset operation $R(r)$ from Section 1.2.2. Since there are infinitely many such operations (one for each choice of $r$), we could not add them all to the toolbox. Instead, you can add your own reset operations to the toolbox!

Let’s practice by adding an operation that resets with probability $r=\frac{1}{2}=50\%$. To start, select ‘Make $R(r)$’ in the menu bar. A new window appears where you can input an angle:

Enter 1/2, and confirm by pressing the button. Congratulations! You have successfully added the $R(1/2)$ operation to the toolbox, which now looks as follows:

To test our new rotation, let us build the following computation in Quirky:

Let’s quickly see that this outcome makes sense. We started with the $[0]=\bigl{(}\begin{smallmatrix}1\\ 0\end{smallmatrix}\bigr{)}$ state. The NOT operation flips the bit into the $[1]=\bigl{(}\begin{smallmatrix}0\\ 1\end{smallmatrix}\bigr{)}$ state. By Eq. 1.27, the operation $R(1/2)$ resets a bit in state $[1]$ with probability $\frac{1}{2}$, that is, it changes the state to

This is precisely what Quirky told us.

In the following exercise you will use Quirky to carry out a more complicated experiment.