Era Quantic | Quantum Computing and Information Articles

 In our previous article, I wrote a general article about what the Fourier Transform does and the Quantum Fourier Transform , which is the application of this beautiful mathematical method in the quantum field. In today's article, we will examine in detail the mathematical representations of the Quantum Fourier Transform. It is very important to know its mathematical notation. Because, our next article, will make it easier for us to understand the application of Shor's algorithm. When we look at it as a definition, Quantum Fourier Transform (QFT) is the base operator that provides conversion from computational bases to Fourier bases.  The important thing at this point is that we use decimal units when doing mathematical calculations. However, when drawing a quantum circuit, we need to convert the decimal expression to the binary system. The table below contains the binary expressions as well as the decimal expressions of the qubit numbers n=1, n=2, and n=3.   If we do this for

 One of the important approaches to solving a problem is choosing the right space dimension. As you can imagine, we cannot solve every problem in the space that we want. However, one of the fascinating things about mathematics is that it allows us to switch between spaces. This mathematical expression, which we know as the Fourier Transform, allows us to solve a problem in another space if we cannot solve it in the space we want, and to return to the space we want with the Inverse Fourier Transform.  The Fourier Transform is a method that has physical real applications, not just abstract mathematics. For example, the Fourier Transform, which converts a signal in the time domain to the frequency domain, has applications in vibration analysis, image processing, sound engineering, etc. On the other hand, if our problem takes discrete values, then what we need to apply is the Discrete Fourier Transform. Our famous space, Hilbert space, which is likely to come to your mind when you say disc

    Another algorithm that has an important place among quantum algorithms is the Grover algorithm. It was developed by the Indian physicist Lov Grover in 1997. I described the Deutsch-Jozsa algorithm algorithm in my previous articles. Although the Deutsch-Jozsa algorithm helps us find the characteristics of the functions and gives us good information about the working principles of the quantum algorithm, it has no application to a real physical problem. Grover's algorithm allows us to solve real physical problems. In this article, I will give information about the working principle of the Grover algorithm and its application as an example. Let's imagine two cities, A and B! Suppose there is more than one way to get from A to B. What we want is to find the shortest path among the existing path options. When we want to solve this problem through a classical algorithm, it will deal with each option one by one with iterations and reach the result. However, Grover's 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 2 n /2 +1 steps for an n-dimensional function. We're going to do some math for |ψ 3 > . When we make a measurement after this process if all of them are 0 as a result, our f functi

  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

  One of the most common uses of quantum computers will undoubtedly be quantum cryptography applications. The basic logic of quantum cryptography is to transfer the desired information securely and quickly between the receiver and the transmitter. This process occurs when the receiver and transmitter create and share quantum key distributions with each other. If an eavesdropper intervenes during this information exchange, one of the assumptions of quantum mechanics, the quantum state vector collapses, and the sent information is corrupted before it reaches the actual receiver. Therefore, the quantum key distribution is very important here. With our current technology, superconducting nanowire single-photon detectors operating at cryogenic temperatures are used. When a small region of the nanowire absorbs a photon, it heats up and temporarily switches from a superconductor to a normal material. This causes an increase in the electrical resistance of the detected nanowire. Once the phot

  Entangled photon pairs form the basis of quantum computers and information. The quantum properties of entangled photons allow us to transmit information faster and more efficiently. However, in order to create this beautiful advantage, some technical problems need to be overcome. Chief among these technical challenges is generating the entangled photons that underpin everything about quantum computers. Within our current technological capabilities, cumbersome lasers are needed to generate the desired amount of entangled photons and precise procedures for long-term alignment are required and their commercial viability is limited. A research team at the Leibniz University of Hannover in Germany and the University of Twente in the Netherlands has succeeded in developing a new technology device that can overcome this fundamental problem. In their work, they developed a coin-sized chip that produces entangled photon pairs. The manufactured chip consists of three main components: a laser;

  With the discovery and development of quantum mechanics, the first quantum revolution has been implemented quickly over time. In the first quantum revolution, we can give examples of technologies such as superconducting and laser that we are mostly familiar with now. However, II. The quantum revolution has also begun to be developed rapidly. II. The fields that make up the quantum revolution are quantum computers and information. In my previous articles, I mentioned quantum quantum computers, teleportation , and cryptology as a start. Today's article will be about the quantum internet. The quantum internet uses the principles of superposition and entanglement, which, like quantum computers, involve strange properties of the quantum. The underlying logic is the same as the entangled qubits that underpin quantum computers. It is aimed to convey the information in this way by transmitting the entangled qubits that form it between the quantum devices. Do not think that we can use

  One of the great potential applications of quantum mechanics is quantum cryptography. According to physicists, quantum cryptography is a safer method for transmitting the desired information, as it uses the logic of quantum mechanics, unlike classical cryptography. What matters in quantum cryptography is quantum keying. For this, basically, two quantum algorithms or protocols have been created. The first of these is the BB84 protocol, which is still used today. This method was developed by Charles Bennett and Gilles Brassard in 1984. This protocol takes advantage of the polarization states of photons. Let's start to explain the protocol through familiar names. Let Alice want to send the requested information, for example, 11010011, to the recipient Bob. Let Eve, our third character, be the person who captures the quantum information Alice sent before it reaches Bob. Alice will transmit 11010011 information, which is made up of photons, to Bob via fiber optic cables. | Let the an