**What are Quantum Computers?**

Why do we need Quantum Computers? Often we listen or read that quantum computer are powerful compared to classical computers. Is this a myth or reality? We will learn about these questions and much more about quantum computers in this article.

Man always wished to get more in less time with little effort and meanwhile struggled to resolve unsolved problems. Although great advancements are done in computing during the last century. But the issues of this era are much more complicated and complex or they may be relatively more complex in the coming days for which really high-power computing devices are needed than our present-day binary computers.

### Moore’s Law and Our present-day Binary Computers

One problem is that the simple switching and memory devices of computers, called transistors, are now coming near the factor wherein they’ll quickly be as small as atoms. If we want computers that might be smaller in size and greater in power than modern days, then we have to do our computing in a significantly extraordinary manner. Entering the area of atoms opens up powerful new opportunities in the form of quantum computing, with processors that might act many folds quicker than digital computers.

### Quantum Computing and Quantum Physics

It seems great but the problem is that quantum computing is extremely complex as compared to conventional computing and operates in the wonderful domains of quantum physics, wherein the classical or Newtonian physics laws don’t work. Quantum computers use quantum algorithms which can lower the computational time slice for some problems using many significant algorithms.

### Why Quantum Computers are so fast?

The precept gain of quantum computation is the speedy parallel execution of commonplace experience operations achieved with the resource of the usage of superposition (entangled) states. To construct a reliable quantum computer, to solve a lot of issues in combination with the utilization of entangled states, the appearance of quantum facts and implementation of algorithms depends on quantum computation.

### Mathematical Model for Quantum Computing

Quantum Turing Machine is used as a mathematical model for quantum computing. But referring to Millennium Problems, planning such a computer that can solve all such problems (P, NP-hard, and, NP-complete) in polytime is still a challenge. This article elaborates on how quantum computation works in a better way than our present-day computers to do numerous excellent things. It is meant to be useful for researchers who are involved to know the ideas of quantum computation in more depth to solve everyday issues and thus this domain is constantly gaining the attention of researchers around the world.

### How Quantum Computers work:

Quantum computing deals with the study of theoretical computing systems which use two very important concepts of superposition and entanglement to process data.[1] Our binary computers or classical computers use memory and the rest of the electronic components which are consisted of transistors. These transistors can process data in the form of binary digits called bits. Binary digits (bits) can only be represented in two explicit states i.e. zero (0) or one (1). Whereas quantum computers work on the sequence of quantum bits i.e. qubits. These qubits are represented in the form of zero (0), one (1), or any other quantum superposition of these two qubits [2]. If we have two(2) qubits, there are four(4) possible states, and similarly, for three(3) qubits, of course, there will be eight (8) possible states as a result of their quantum superposition.

## Quantum Computers are powerful

Thus in the more generic form, we can say that the superposition of n qubits will generate 2^{n} states simultaneously. It is a breakthrough of quantum computers over binary computers because the latter can exhibit only one of the states at a particular given time.[3] The manipulation of qubits is done by a specific pattern of gates which is also called a quantum algorithm. These algorithms are challenging as they provide solutions with a particularly known probability. The typical representation of deployment of qubits in a quantum computer for particles having two particular spins i.e. ‘up’ and ‘down’ is given

## Quantum Computers are powerful

Basically, quantum computers having a certain number of QUBITS, operate in a quite different way as compared to a digital computer with equal bits. To represent the state of the * n* QUBITS system over the classical computer needs space of complex coefficients whereas to represent the state of

*bits on the same computer requires only n bits. Thus computers, based on qubits, can store more data as compared to binary computers. To grasp the working of a qubit, let us consider a classical computer having a 3bit register. If the exact state of this 3bit register at a particular given time is unknown, then it may be expressed as a probability distribution on eight (23=8) different 3bit strings i.e 000, 001, 010, 011, 100, 101, and 111.*

**n**## Quantum Computers are powerful

Thus the behavior of the superposition of qubits provides ** Hilbert space** which is one of the biggest advantages of quantum computation over traditional classical computation. In the case of quantum computers in which these states are exactly known, then, of course, there will be one of these given states with probability 1. But in the case of classical computers, the probability of all these states is equal.

More precisely a qubit can be denoted in the following three ways;

- Two different polarizations of a photon.
- Aligning a nuclear spin in a uniform magnetic field.
- Two electronic levels orbiting in an atom.

In the atomic model, an electron may exist either in-ground** **or

**state represented as**

*excited*|0> and |1> respectively as shown below;

But the quantum theory says that electrons can attain an intermediate state represented by |+> while moving from the |0> (ground state) to |1> (excited state). Similarly, the state of a 3bit quantum computer is described as an 8-dimensional vector given as (a_{0},a_{1},a_{2},a_{3},a_{4},a_{5},a_{6},a_{7}). where the coefficients a_{k} are called complex numbers. Thus we must have

And for a certain value of ‘k’, the probability of the system in k^{th} state is given by |a_{k}|^{2}. Depending upon the space basis, a given 8-dimensional vector can be represented in various ways such as the state (a0,a1,a2,a3,a4,a5,a6,a7) on the computational basis can be written as;