English

Quantum Algorithms  (Part 1)

Abstract

Quantum computation uses quantum mechanical phenomena to describe the quantum computation. Superposition and Entanglement are the most basics and fundamental concepts in quantum mechanics. So using these concepts it is capable of implementing a quantum computer models and algorithms turn on them as well. So there is no doubt about how quantum nature affects the quantum algorithms. There is a tendency to replace of algorithm of classical version to quantum version because of their native ability of efficient computation. It is also experimentally shown that this not only true for theoretically using the recent achievement of the quantum computer implementation. In this way it is not difficult to think that quantum computation algorithms are very interesting and make many things faster than ever.

Introduction 

Before we talk about quantum algorithms we should know what an algorithm is initially. There are many algorithms developed by humans within the last few centuries in history.  As we always say every creation of a human is not built in a vacuum. They are built in their own mind. Any human life in a particular society and this society has a main culture (main stream). So we can never say that our so called creations are absolute (exits without other nature). Everything is combined to other things (concepts) and one thing can depend on other things. In General If A and B are two concepts there can be circular relationships like A depends on B and B depends on A. you might wonder why I don't directly talk about quantum algorithms and talk about other things but that man doesn't know that quantum algorithms are built on one culture and it will always be useful to know about that culture to understand some natively difficult problems in that knowledge system.

Any way what is an algorithm is very important question. Why is an algorithm important? How many algorithms are in computer science? Are there two or more algorithms for the same problems? Can we come up with our own algorithms?  These are some question will be in your mind up to now. Let’s try to get some of them and discus for an extent.

An algorithm is a human made story (solution) for our problem(s) encounter when we are going to get the knowledge in an abstract manner. So we get thing in an abstract manner. Why we would not likely to find answers in a concrete manner most times. This can be understood by a simple example. We know it is not a difficult thing to add given numbers. We know one plus two is equal to three and so on. But we cannot predict the result of one plus two plus three plus four plus five within the above result. It is only a concrete solution given to add two successive integers. Suppose we get this problem in an abstract sense and we can propose this solution for n number of successive integers. The addition of any number of positive successive numbers start from one is equal to n times n plus one divided by two (n (n+1)/2). Now the answers for the above problem is very easy we should know only how many successive numbers are to be added and are they actually in a proper order.  If the first 100 numbers is our guess the answer is 5050.Now look how our answer is easy. This is very simple example. The Factorization problem is also such a problem use for cryptographic algorithms like RSA algorithm and many algorithms are given for factorization up to now in mathematics. Other thing is there can be many algorithms for one problem. Their feasibility depends on their computational steps. And is also a measurement of time. So for generality we say algorithms are feasible or not depending on their computational steps given to solve problems. Computer complexity is the subject discus about these problems in depth.

So now we have a basic idea about what an algorithm is and why it is important in an abstract scene. Now things get more and more abstract than before. We don’t consider about what is given to the algorithms and what output is given back for a problem. It can be identified a process which get inputs and give relevant outputs. Within this general idea we can discuss further about algorithms in the interest of quantum computation and some classical algorithm may be our topics as necessary to understand the concepts correctly.

Basics Concepts

there are two most interesting concepts in quantum mechanics are called superposition and the entanglement. Actually I think the idea that it is important to have sufficient knowledge about mathematics to understand these concepts in quantum mechanics. However within this idea in our mind there is no way of stopping us to talk about them as simple as possible without harming the meaning of these concepts.

Quantum superposition principal says that a (quantum) particle can exist in several place in the space at the same time in a wave like nature. Here wave like nature means the current states of a particle in a superposition is in a wave. This is analogous to the case where lots of particles contribute to create a wave. What we can only do is to give a probability for a particle to be in one of its superposition states. So this is completely against of the classical physics and this indeterminism makes lots of people in trouble.

Then our interest is more mysterious behavior that describe how quantum particles may work together(interact).It is said that when two quantum like particles belong  to the  same system and when they are separate in any distance they work still together. In simple what we do to one particle will be instantly affect to the other particle may be in the end of the universe. Once Albert Einstein said this is completely misinterpretation of the physical nature. Einstein also said the speed of information is not more than the speed of light. It is reasonable to think why he said so.

However these concepts cannot be ignored because of the experimental result given up to now. Within these stories, it can be described those experimental results. So it is no way to blame when things go against the classical physics.   

Quantum Bit

Now the main concern about quantum computation is why there is two way of computation. In general we know that coming knowledge system have to fulfill failures of the previous system. Sometimes we say it is a paradigm shift in the history of that continuous knowledge. That is why quantum computation is important when classical computation cannot solve problems in a feasible way.

No doubt quantum computations use the properties of the so called quantum nature. The models we propose of computation should basically address the phenomena of superposition and the entailment of quantum particle.

Most elementary concept of classical computation is the bit. But this is not exactly similar in quantum computation. Refusing the bit but giving quantum bit makes a new drama in computation.