Past, Present and Future of Quantum Computing: A Systematic Study

Quantum Computing is relatively new and it's kind of a special type of computing that uses the laws of quantum physics. In classical computing, we have some limitations and we can overcome those with the help of Quantum Computing as it uses qubits, but we need to keep those qubits at low temperature. Quantum Computing uses the probabilistic nature of electrons. The power of a quantum computer increases exponentially with the number of qubits linked tougher. Quantum computers are very difficult to make but there are a huge number of calculations that can be done easily with the use of a quantum computer. Quantum computers are way better and faster than classical computers. So, we can say that quantum computers rather than quantum computing will be used in the near future to replace classical computing.


I. INTRODUCTION
In the year 1927, 29 scientists gather in Brussels to discuss physics. Those few days, they wrestled with the question of quantum determinacy and whether our world at the minutest level operates as a fixed system or merely as a group of probabilities. They discuss the problem of light. For nearly three centuries since Newton wrote his famous treatise on optics, physicists had debated whether light was a particle or a wave. At first, Newton told, that light is a rain of particles. Later Planck postulated that the energy of light is proportional to the frequency, and the constant that relates them is known as Planck's constant (h) [1]. His work led to Albert Einstein determining that light exists in discrete quanta of energy, or photons. In 1803, this argument was thought to be put to rest by the mostsimple experiment that ever created, The Double Slit Experiment. Then it was clear to all that the photon has dual nature of particle and wave.
From this point, physics is divided into two parts.
One is Classical Physics and the other one is Quantum Physics. Later they saw that the electron has two properties, "Superposition" and "Entanglement". And these can be enlightened with the help of Quantum physics rather than Quantum Computing. Quantum  In 1994, Peter Shor developed his algorithm [14]that allowed quantum computers to successfully process large numbers much faster(exponentially quicker) than the best old algorithm in traditional machines.
From here the journey of Quantum Computer and Quantum Computing has started.
In electrons or photons, they have the property of being able to exist in multiple states is known as Superposition.This means that a single qubit can be described by a linear combination of |0> and |1>. It is also called as Mixed State.
It is denoted as | Ψ > = α | 0 > +β | 1 > Quantum Entanglement is a physical phenomenon that occurs when a group of particles is produced, interacted, or shared in close proximity in such a way that the quantum state of each particle can be explained without the form of others, including when the particles are separated by a large distance. A supercomputer has a high level of performance compared to a classical general-purpose computer.
We can measure the performance of a supercomputer  deterministic. Data processing is done by logic and in a sequential manner.

III. SUPER COMPUTERS
As we know there are some limitations of a classical computer so the concept of supercomputer came. A supercomputer is a type of large computer with the resource of multiple computers [10]. It is a very large size computer. These types of computers are expensive to build because here we can't add or remove any components from the supercomputer.

IV. HIGH-PERFORMANCE COMPUTERS
High-Performance Computer [11] is generally used for higher performance, here we arrange the power of a computer in a way that it can perform much better than a typical classical computer. This type of computer is used for solving larger problems in various fields. Basically, here we combine more than one Super Computer and parallel computing techniques to achieve the desired target.HPC is cheaper than supercomputers because we can easily add or remove components here.

V. INTRODUCTION TO SUPERPOSITION
let's focus on the two properties of electrons and for the experiment purpose, call them Colour and Hardness. The only observable colours are "black" and "white" and the only observable hardness are "hard" and "soft" (binary properties). These properties can't take any other observable values. So, here we have a colour box and a hardness box which will measure the colour of the electron that is either white or black and the hardness of the electron that is hard or soft.

fig1: Colour Box and Hardness Box
This colour box has three apertures, one in port and two out ports (one which sends out white electrons and the other sends out black electrons).
This hardness box has three apertures, one in port and two out ports (one which sends out hard electrons and the other sends out soft electrons).
One key property of these colour boxes and hardness boxes is that they are repeatable. And as we will see later, using Bell's inequality, we can confirm that such things do not exist. Now, let's take a Hardness box and set two mirrors in the path of the two out port and add a box that will combine the beams together into a single beam and we'll send the output into a hardness box again. We are passing random white electrons into the hardness box. And the result of this experiment will be we'll have a 50-50 ratio of hard and soft electrons. Now, let's take a Hardness box and set two mirrors in the path of the two out port and add a box that will combine the beams together into a single beam and we'll send the output into a colour box. We are passing random white electrons into the hardness box.
But we got a wall on the way of the soft beam so, it'll observe the soft electrons. And the result of this experiment will be we'll have a 50-50 ratio of black and white electrons. It is also called as Mixed State ( |Ψ > = α | 0 > + β | 1 >).

Ⅵ. INTRODUCTION TO ENTANGLEMENT
Entanglement [13] comes to play when we have two non-interacting particles.
These two non-interacting particles can have a limited distance or they can have an infinite distance between them. A strong interaction between particles is not required to produce the entanglement property of electrons, these particles can be non-interacting.
Let's assume particle 1 can be in states u1 and u2, and particle 2 can be in states v1 and v2. These are the possible states of particle 1 and particle 2.
So we know that these two particles are not interacting, We can tell what particle 1 is doing and what particle 2 is doing. First, assume that particle 1 is doing u1 and particle 2 is doing v1 and mathematically, we like to make this look like a state, and we want to write it in a coherent way. So, we are going to multiply these two things but we must say sort of multiply because these are vector states, here we put something called a tensor product [⊗].
So, it'll look like this -> |u1>⊗ |v1>, here we don't move things across and this is a possible state. Now, we could have a different state. Because particle 1 and particle 2 could be doing something different. particle1 -> α1 |u1> + α2 |u2> The rules of tensor multiplication to combine those states are just like a product, except you never move the states across. So, from the above tensor operation, Here, what the first particle is doing depends on the second particle and what the second particle is doing depends on the first particle. This is an Entangled state.
If we take two particles with spin, for example, we can build entangled states of two spins 1/2 particles.
And this state will look like this -> If we say, Alice has one particle, Bob has the other particle, maybe Alice is on the moon with her electron and Bob is on the earth with his electron and We have two accepts here- Removing the physics of out-of-time-order correlators.
Dynamic Information in Complex Quantum Circuits.

J. Beyond the performance of classical computing
Google's Sycamore quantum processor was able to do a job in 200 seconds that could take 10,000 years on an old computer. We set up a quantum computer and the world's most powerful supercomputer (at the time) to select random 0s and 1s randomly, and to measure how random it was. This may not seem to be very useful, but computing is a difficult computer task. It was the first time that any quantum computer had successfully reached this milestone.

K. Towards a Quantum Computing Future
By working with universities and research institutes, Google is making an important contribution to ideas and algorithms that we can use for computercorrected computers when we get there.
They will continue to discover new, increasingly complex problems that can be successfully tested by our computers in quantum NISQ computers over older computers. released the long-awaited quantum imitation toolbox [7]. This is also the first 'Quantum Computer Simulator (QSim) Toolkit' in the country. According to the report, IISc Bangalore, IIT Roorkee, and C-DAC have teamed up for the first time in India to address a shared issue of expanding the boundaries of quantum computing research nationwide [8]. The great advantage is that researchers and students will be able to perform quantum computing research effectively using this device.
The toolkit will enable researchers and students to study quantum computing effectively. The QSim project -jointly developed by IIT Roorkee, IISc Bangalore, and C-DAC -will help develop and refine quantum algorithms. which are important in their performance but yet disintegrate before any irrational system has a chance to run until it is completed.
(iv) Qubits can't store data or a set of data for a long time, so this is another problem with quantum computers nowadays.

ⅩⅣ. CONCLUTION AND FUTURE SCOPES
In the near future -perhaps within 5 to 10 years, but who knows, maybe a lot sooner -quantum computing will be at a stage where it can be used to solve problems that improve our lives, on an everyday basis -Intel's head of quantum research, Jim Clarke, calls this "quantum practicality. [5]"Quantum computers won't be able to replace classical computers for now but in the case of the near future maybe it'll be possible to replace classical computers with quantum computers. This is kind of similar to older computers, such as the mainframes created by IBM in the mid-20th century, which did not become operational for everyday use until universal operating systems and programming languages were discovered.
Currently, quantum computer control systems fill a small room -this efficiency reduces it to a single chip in the near future. Once this value has been proven, experts hope that quantum computers will be used to build systems that help us cope with climate change.
One of the ways in which this can be done is to create new types of agricultural fertilizers. Switching to new compound fertilizers can reduce the earth's natural gas consumption by 3 to 5 percent. This will be done by building new auxiliary molecules that are more efficient at creating the necessary chemicals.
Quantum computers also have a huge impact on machine learning and learning. These computerassisted computer systems -which include learning programs and improvements in their operationsoperate using large neural networks, requiring high computer computing. Quantum-powered AI will provide us with devices that can think and learn faster than before. This will enable more advanced systems to be replicated and modelled. Imitation is based on our understanding of reality, in order to replicate the rules within our models. This means understanding the behaviours of an object and the quantum level. Richard Feynman [6], a Nobel Prizewinning physicist who has helped to explain much of what we know about quantum, argued that only quantum computers could be powerful enough to accurately measure quantum function.If this were possible (and would require quantum computers much more powerful than the ones we have today, instead of thousands of qubits), we should be able to build models that accurately replicate the most sophisticated systems that can be modelled todaysuch. such as electromagnetic radiation, gravity, and perhaps even the biological brain.Whatever the case, it is clear that quantum computing is an exciting field of technological advancement, and we can expect to see it grow and impact our lives over the yearsperhaps in as important a way as the advent of computers in the last century, and growth of the Internet in this century.Quantum Computing won't be able to consume the world of computing but surely enough will have a major impact on the computing universe for the next couple of decades and will