Deutsch–Jozsa Algorithm

In our previous article, I mentioned the Deutsch algorithm, which is the first of the quantum algorithms. In this article, I will talk about the Deutsch-Jozsa algorithm.

In fact, if you look at it, this algorithm is an extended version of the Deutsch algorithm. Extended means an algorithm that can be applied to n functions.

It is almost the same in formulation, only revised according to n functions.

Let's examine it in more detail!

Let's define a function that maps 0 and 1 to 0 and 1.

We will also ask the question that we have emphasized in the Deutsch algorithm and which constitutes the main problem of this algorithm.

In how many steps can we determine the characteristic of our function f in the example above?

When we consider this problem in the classical algorithm, it will determine

2ⁿ/2 +1 steps for an n-dimensional function.

We're going to do some math for |ψ₃> .

When we make a measurement after this process if all of them are 0 as a result, our f function is fixed, but if we get 1 from the measurement results, we can say that our f function is in balance.

Reference

https://www.youtube.com/watch?v=MZD3gYBg0_c&list=PLqNc_xpYGu775P7iJA7Kvfxmv_Fm9wwHj&index=3

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