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Deutsch Algorithm

 

The Deutsch algorithm was discovered by David Deutsch in 1985. The main motivation for this algorithm is the problem of how many steps to determine the characteristic of a given function.

Classical computers, therefore, classical algorithms can determine the character of the given function in at least two steps. Because, as you know, classical computers are made by processing the 0 or 1 bits separately.

However, for the solution to our motivation problem, the characteristic of the function can be found in one step by quantum computers, that is, by quantum algorithms. As a result of measuring our qubits in superposition, as a matter of fact of quantum physics, enables us to reach the desired result in one step.

As David Deutsch said “Computers are physical objects, and computations are physical processes. What computers can or cannot compute is determined by the laws of physics alone. . .”

Let's take a basic look at this easy algorithm.

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

 

Let this function have the following characteristics;

It solves the characteristic of the function defined above in at least two steps.

With the quantum algorithm, I wrote below, the characteristic of this function can be solved in one step.

Now let's pass the state vector |ψ2> through the Hadamard operator.

Finally, when we measure the state vector, we find that if we get |0> it is a constant function, and if we get |1> we find that it is a balanced function.





Reference

https://people.vcu.edu/~sgharibian/courses/CMSC491/notes/Lecture%206%20-%20Deutsch%27s%20algorithm.pdf

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