Fundamentals of Quantum Computing

Some History & Basics of Quantum Computing : 

There is lot going about Quantum Computing in Industry of AI & Data Science. So, today’s topic is to understand about Quantum Computing from complete literal ZERO in very narrative and simple way!!! 
Let's start with the word “Quantum”. 
What is that?
So traditionally, the word Quantum is used when we are thinking of something tiny. 
That is, we all have learned physics till 10^th or till +2 or most probably till Engineering. So, Physics is basically something which studies about visible universe. i.e. which is there after atom. But later on, there was a newly introduced branch of physics which we refer as “Quantum Physics”. Now a days this “Quantum Physics” thing is very Trending!!! Right? 
Yes!!! 
So, what is that? 
What was a motivation behind introducing such new branch if there is already physics? 
So, basically as stated earlier, Physics is all about conceptualizing and analyzing the things which are visible i.e. which comes after atom. 
On other hand, Quantum Physics is a branch which tells us about what happens inside atom!!! 
Does it make sense?  
So, moving forward, Quantum Computing is something when we use concepts of Quantum Physics for analyzing & computing something. Now the question arises. 

What is the difference between Quantum Computing and Traditional / Classical Computing? 

So, let's see the difference table:

So, we can clearly see that the major difference is unit of Traditional Computing is Bit (either in state 0 or 1). whereas Quantum Computing is having basic unit Qubit. Now, in nutshell lets understand what is Qubit? 
Bit is something which can either be 0 or 1. But Qubit holds probability distribution of being 0 and 1 simultaneously. Like without measuring we cannot say that in which state Qubit is present. Once measured Qubit breaks down into 0 or 1. I believe you are getting my point!!! 
Now there are 5 main components of Qubit. Let's understand that!!! 

So, readers, till here you are on some introductory level for understanding of Quantum Computing. Here we are ready for jumping into Research Paper on Quantum Computing by Massachusetts Institute of Technology (MIT). 
Let’s Go!!! 

Abstract:

In Abstract of Research Paper, All the modern benefits of Quantum Computing are mentioned. 
This Research Paper by MIT is basically to introduce Quantum Computing with its technical terms so that Industry people can easily implement this technology to solve their problems more efficiently and with more accuracy. 

Introduction: 

A recent study shows that global market value of Quantum Computing by year 2035 will be around USD 1 Trillion Dollar in sections like finance, chemical industry, pharmaceutical industry and automotive sectors. Additionally, Largest tech companies like IBM, Google, Microsoft, Amazon, Alibaba are already investing billion dollars in R&D of Quantum Computing. This companies often provide access of their Quantum Computers to public via cloud infrastructure. 

So basically, Quantum Computers use concepts of quantum mechanics like superposition and entanglement to represent data and performing operations on them. 

Note – Here Superposition and Entanglement refers to the terms mentioned previously. 

Some Chinese scientists claimed that quantum computers work 100 trillion times faster than a normal traditional computer. 

Quantum Computing Systems: 

Rough Architecture for Quantum Computers: 

So basically, even in Quantum Computers, to input and output data, Normal Traditional Computers are used.  
Von Neumann Architecture here is representing traditional computer with CPU. Once processed from traditional computers, Output device is then connected with Quantum Computers to get data inside them. 

As explained earlier, Classical bit can only be in either 0 or 1. Whereas Qubit can exist in both 0 and 1 simultaneously with specific probability. Now, Lets understand each component of quantum system systematically. 

1. Hardware Layer:  
   As mentioned earlier, Classical Traditional Computers use Bits to store information while Quantum Computers use Qubits to store it. So very basic difference between Bit and Qubit is In Bit, either we can store information as 0 or 1. But in Qubit have “probability” of information being 0 or 1.  i.e. Qubit can be 0 with 85% probability and 1 with 15% probability. So, here’s the question arises…. what does it really mean? Like, being “1” for 15% and “0” for 85%? Which advancement this kind of probabilistic measure is going to do in our calculations?
    
   Let's understand this by simple example:  
   So, just imagine a scenario where user forgot his password. Just for now assume that we are having designed system which is going to check password of user from available metadata of user (like name, birthdate, hometown and so on).  So, if this system is traditional / classical computers, then that system will one by one check possible passwords for User to help him with correct password. Right???
    
   But iff the system is containing Quantum Computers; System will check all possible passwords of User with definite probabilities in one single instance!!! And when you are asking system which is correct password? 
   System will give answer which is having maximum probability!!! 
   Does that make sense now? 
   So, it's actually doing work of n steps in one single instance by reducing time and increasing efficiency with high magnitude!!! 

Generally, two types of hardware's are used for Quantum PCs: 

1. Analog Quantum Computing  
   Uses natural quantum processes to solve problems. Use Case – Solving optimization problems, Like finding best route for delivery trucks. 
2. Digital Gate-Based Quantum Computing  
   Uses Quantum GATEs  
   Companies like IBM and Google use this approach to solve a wide range of problems, from simulating molecules to cracking encryption.

Some preliminary Quantum GATEs: 

1. Hadamard Gate (H Gate) 
   This gate turns qubit from definite state 0 or 1 into a 50-50 mix of both. 
   Why it matters : 
   This Gate creates superposition, letting the qubit explore multiple states at once. 
2. CNOT Gate (Controlled Not Gate) 
   This Gate links two qubits so one controls the other. 
   In pair of these two qubits : 
   One is Boss qubit – Acts as a boss which controls the target qubit. It target qubit is 1 boss qubit flips it. 
   If its 0, boss qubit don’t do anything. 
   Target Qubit :
   Obeys the signals of Boss qubit. There are many gates in quantum computing, but unfortunately that’s not our focus right now. So Readers, Let’s move on to the software layer of quantum computing. 
   Software Layer : 
   So as like other systems, Software Layer is interface between user and hardware layer. This layer has to cope with challenges of the thermodynamically unstable quantum states. It actively reduces thermal noise within and around the quantum system and performs error correction procedures.  
   For example, quantum computers and especially digital gate-based ones are highly sensitive to changes in the environment, such as vibration, temperature fluctuations, etc.  
   Noise in quantum computers can also be caused by imprecise control of the quantum hardware or manufacturing defects. 
   Quantum states are sensitive, so errors are common. To fix this, multiple physical qubits are grouped together to create one reliable logical qubit. And the major fact is quantum computers need to be cooled at -273-degree Celsius OR 0 Kelvin  
   (SI Unit of Temperature). 
   Application Layer: 
   Unsolved problem for quantum computers now is not having efficient quantum memory. There are some proposals to make QRAM which is equivalent to RAMs in traditional computing. Now to store any information in quantum computing there is only one way and that is storing calculation of each qubit. But it is a lengthy process.
   
   Now there are certain algorithms in quantum computing to search information from specific qubit: 

1. Grovers Algorithm: (Known as quantum search algorithm) 
   – Simply speaking this algorithm go through N/2 items if there are total N algorithms. 
   – So steps reduces approximately to (N)^(0.5) 
2. Shor’s Algorithm : (Knowns Integers Factoriazation Algorithm) 
   – Can factorize integers than any present classical algorithm 
   – This algorithm is basis of RSA encryption  
3. HHL (Harrow Hassidim Lloyd) :  
   – Used as quantum algorithm for linear system of equations. 
   – Algorithm can estimate result of a function of the solution x of linear system (Ax = b), where A is matrix and b is vector. 

Table : Major uses of quantum computing in AI & DS 

Current Uses of Qunatum computing in different fields (Information Systems , Health care, pharma industry) & Conclusions : 

1. As quantum computers are best with simulation, they are used in pharma industry by IBM & Google by simulating minute interactions of molecules for drug development. 
2. As quantum computers calculate to many solutions at one instant they are very well versed with solving optimization problems . Volkswagen used a quantum computer to optimize traffic flow in Beijing, reducing congestion by calculating the best routes for thousands of taxis simultaneously. 
3. Used widely for Cryptography and Cybersecurity  
   – China launched the Micius satellite in 2016, which uses QKD (Quantum Key Distribution) to enable secure communication between Beijing and Vienna. 
4. Machine Learning 
    –  Researchers are exploring quantum versions of classical algorithms, like support vector machines and neural networks, to improve tasks like image recognition and natural language processing. 
   Hence this may get rise to Quantum Machine Learning. 

So, Readers I believe you got introductory idea of quantum computing and difference between quantum computing & traditional computing.