Quantum Computing

Quantum Computing

Moore’s Law states that the number of transistors integrated on a silicon chip doubles every year. By 2020 to 2025, the size of the transistor will be too small and it will generate heat that cannot withstand by the conventional silicon technology.  The number of transistors that can integrate on the chip reaches its maximum. The speed of the devices will reach its limit. The current INTEL uses 32nm silicon technology. If scaling progresses, it will reduce the size, then the electrons start tunneling through micro-thin barriers between the wires corrupting the signals.

History

In 1982, physicist Richard Feynman proposed the idea of creating machines based on laws of quantum mechanics instead of laws of classical physics. In 1985, David Deutsh published a paper which describes that quantum circuits are universal. He describes about the universal quantum computer. In 1994, Peter Shor derived the first quantum algorithm, to factor the large numbers in polynomial time. He used entanglement and superposition properties of quantum mechanics to find the prime factors of integers which are used in the quantum encryption technology.  In 1997, Lov Grover developed a quantum search algorithm which is very faster. After that, David Cory, A.F.Fahmy, Timothy Havel, Issac Chuang, Neil Gershenfeld published a paper about quantum computers which is based on bulk spin resonance or thermal ensembles. In 2001, researchers used Shor’s algorithm .In 2005, scientists built a semiconductor chip ion trap which lead to scalable quantum computing. In 2007, first commercial quantum computer demo was published by D-wave on Orion system called superconducting adiabatic quantum computer processor. But the scientists said that it did not achieved the quantum speed yet. They are not sure that this system is efficient than conventional computers. Research is still going on. Figure below shows the world’s first commercial quantum computer built by D-Wave systems.

                                                             Quantum Computing Processor

First solid state quantum processor is built in 2009. Researchers created a silicon chip based on quantum optics that runs Shor’s algorithm. Further modifications are made in 2010. In 2011, Scientists made quantum teleportation.  Teleportation is the technique used for transfer information in the quantum level without any signal path. In the same year D-wave systems first commercial 128 qubit  processor. In 2012 IBM scientists said that they had several findings in quantum computing with superconducting integrated circuits. In 2015 they had further advancements towards the realization of practical quantum computer.

Quantum Computing

It is based on the theory of quantum mechanics. Quantum mechanics is the study of small objects (nanoscopic scales). It overcomes the inability of classical mechanics.Quantum mechanics provides mathematical description of dual particle like and wave like behavior. Atomic theory and corpuscular theory of light are the earliest versions of quantum mechanics. It produces high accurate output. Quantum mechanics is on the basis of quantum theories of matter and electromagnetic radiation. It explains the nature and behavior of energy and matter on the quantum. It uses the quantum mechanical phenomenon for the operations on data. These operations done at atomic or subatomic level.  Classical mechanics deals with the macroscopic system while quantum mechanics deals with the microscopic system which is in atomic and subatomic level. The first generation of computer uses vacuum tubes, the second generation computer is based on transistors, the third generation computers are based on IC (Integrated circuits) and the fourth generation computers are based on the micro processors. The sizes of the computer system (components) are reduced and at last the classical theory will fail to explain. This explains the essentiality of quantum theory. Quantum Computer is the computational system which directly uses quantum mechanical phenomenon to perform operations on the data. The superposition and entanglement are the quantum mechanical phenomenon used by the quantum computers. The computational operation performs on quantum data which is called as Qubits. The quantum computers are entirely different from the classical computer based on transistors.

In classical computers, the data are encoded in to binary digits, either 1 or 0. The classical computer process only binary information. That is either ON state or OFF state. But in quantum computation, it uses quantum bits (Qubits) are used for encoding the data.  So it can encode infinite amount of information. It uses both ON and OFF at the same time. Consider a situation; trying a calculation  with a lot of different numbers to find the correct one.  In classical computers, it tried each number in each turn which takes time for computation. In quantum computer, it can try different numbers simultaneously by using the superposition of states which increases the computation speed and accuracy.

The classic computer performs operations by using logic gates while quantum computer uses quantum logic gates. The qubit is the unit of quantum information. The physical objects such as electrons, atoms, etc uses the qubits. It can exist as either 0, 1 or superposition of 0, 1 at the same time. A single qubit has any  quantum superposition of 2  states. A pair of qubits has any quantum superposition of 4 states. Three qubits has any quantum superposition of 8 states. Generally, a  quantum computer with n qubits has 2^n different states at the same time. The quantum computer operates by intitially setting the qubits in a controlled initial state. These qubits are manipulated by using fixed sequence of quantum logic gates. The particular sequence of quantum logic gates is called quantum algorithm. At last they provide the correct solution.

The qubit uses two energy levels of an atom. They are excited state and ground state.

Properties of quantum mechanics

• Superposition

The single qubit forced into superposition of 0 and 1 simultaneously which can denote by the addition of two state vectors. The qubit of superposition can exist in both states at the same time. Two particles overlap each other without interfering each other. Polarization of single photon is an example. It has the propery of exist in multiple states simultaneously. In the quantum system, If the particle have states a and b, then it also have the states α1a+α2b, whereα1 and α2 are complex numbers.

• Entanglement

It is the most important property in quantum information. It can exhibits correlation between states which are in superposition. That is, in quantum mechanics, the properties of particles can be changed even if there is no direct interaction between the particles. If the particles are linked, then the change in property of one particle will affect the another. The particles can linked and change the properties without having direct interaction. After that, the states of two particles are called entangled. Consider two qubits exist in the superposition of 0, 1 state.The measurement of one qubit is always correlated with the measurement of another qubit if the qubits are entangled.

Quantum Computer is a machine which performs calculations based on the quantum mechanics .It is like the classical computer which cannot use transistors and diodes. The single atom transistor lead to the building of quantum computer which is controlled by electrons and qubits.

                                                     Quantum Computer

In 1930, Quantum Turing machine developed by Alan Turing  is the theoretical model of such computer which is known as universal quantum computers. Todays computer can only manipulate one of the two bit 0,1. Quantum computers can encode the qubits exist in the superposition. Qubits represents atoms,ions, electron and control devices that working together will act as memory and processor. The quantum computer uses the multiple states at the same time, so the quantum computers are much efficient than traditional computers. The quantum computers composed of given number of qubits  is fundamentally different from same number of buts composed by classical computers.The classical computer requires storage of 2^n complex coefficients for representing n qubit system. So it is clear that  qubits can hold more information than classical computers.

Consider a classical computer that can operates on three bit register. Then the different states are 2^3=8. The different states are 000,001,010,011,100,101,110,111. In case of deterministic computer, the computer is in exactly one of these states with probability 1.  In the case of probabilistic computer, the computer  is in any one  of the possible states. Let the probabilistic states are A,B,C,D,E,F,G,H;where A is the probability of state 000,B is the probability of state 001,and so on. The sum of these probabilities must be 1.

Similarly the states of three qubit quantum computer can be considered as a,b,c,d,e,f,g,h.  The coefficients of three bit quantum computers have complex values. The sum of squares of coefficients magnitudes must be equal to 1. i.e,  IaI^2 + IbI^2+….IhI^2=1. The probability of each state is represented by squared magnitudes. The complex number encodes magnitude and directions in the complex plane. The phase difference between any two states (coefficients) represents a meaningfull parameter. This is the fundamental difference between probabilistic classical computer and quantum computer.

The three bit state in classical computer and three qubit state in quantum computers are  eight dimensional vectors. But these bits are manipulated to perform operations in different ways.  In both cases the systems must be initialized. i.e, In the case of classical computers, the sum of probabilities must be 1. In case of quantum computers, The sum of squares  of states must be 1. After execution of algorithm, the results are read off. In classical computers, one three bit state is obtained from the samples of probability distribution of states. In quantum computers, three qubit state are measured ( quantum state equivalent to classical state by squaring the magnitudes of quantum states)which is the sample from distribution.  This destroys the original quantum state.  By repeating the processes such as initializing, running, measuring of quantum computer result will increases the probability of getting correct answers.

The transistor replaces vacuum tubes. Quantum computers will replaces silicon chips. Most of the quantum computing research is still theoretical. Still the most advanced quantum computers cannot manipulate the qubits beyond a limit. Researches are going on to develop the quantum computers.  It can solve problems very faster than classical computers by using the best algorithms such as Shor’s algorithm. The Shor’s algorithm solves discreate logarithm problem and factorization of integers in polynomial time. Scientists already built quantum computers to perform certain calculations. But it takes ten more years to build the practical desktop quantum computer. It can use for several applications such as communication, security, and encryption purposes etc.

Advantages of Quantum Computing

• The computing speed and accuracy increases.
• Highly secure communication is possible.
• High efficiency compared to classical computer.

Disadvantages of Quantum Computing

• The quantum systems are too small.
• To measure the properties of quantum system without disturbing it is impossible.
• It is impossible to predict the properties of a particle in the quantum system.
• Qubit possess in different states (many values), but it produces only one result  for one execution.
• Different execution required to produce the desired output.
• It is impossible to copy the qubits.

Applications of Quantum Computing

• Factorization: - For classical computer, the integer factorization of large integers ( product of prime numbers) is difficult. But quantum computers can solve this problems using shor’s algorithm. So the quantum computers can used in cryptographic applications. It is  useful for encoding and decoding of secret information. It is highly secure. The third party cannot read the message. The current encryption methods are simpler. So the information sent through internet  are not safe.   Quantum computer can easily break the encypted messages used today.
• Solving complex mathematical problems.
• Searching huge amount of data :- Quantum computes can find something from large amount of data. for example, To find two equal numbers from a large amount of data, the classical computer have to try all numbers which needs lot of steps. The quantum computer can do it with few steps.
• Google image search
• Teleportation- Technique used for transfer information in the quantum level without any signal path.
• Ultra- Secure Communication- By quantum computing, more informations are  encoded and transmitted. It is possible to transmit information without any signal path. So there is no interfere path for extracting information.
• Error correction and error detection can be improved.
• Quantum Networking which uses internet and intranet networking.
• Molecular simulations helps pharmacists and chemists to study about the interation of products with each other  and with biological processes.eg:- drug interact with disease.
• Accurate weather forecasting - Quantum computing can analyze all data and give better idea about when and where the bad weather occurs.It  will help for taking preparation to save millions of lives before  natural disasters occurs. Also it helps to take precautions to prevent the disasters.

Accurate weather forecasting - Application of Quantum computing 

• Discovery of new drugs.Molecular simulations helps pharmacists and chemists to study about the interation of products with each other  and with biological processes.eg:- drug interact with disease. Chemists have to test the several molecular combinations for finding the best one which can prevent disease. It is an expensive process and also needs many years. By using the quantum computing, it try different molecular combinations and find the best one.It will reduce the cost and time for developing new drugs.
• Traffic Control- The quantum computing can quickly calculate the optimal route.The quantum computer can compute the length of all routes simultaneously and quickly finds the best one.It can control air based and ground based traffic.

            Traffic Control- Application of quantum computing 

• Military and defence purposes- Satellites collecting millions of images and videos. It is difficuilt to analyze by a classical computer. But the quantum computer can sort this images a faster as a classical computer.
• Space exploration- Using keplers space telescope, astronomers discovered over 2000 planets outside our solar system. The quantum computer can spot more planets and give more information using the telescopic images.
• Artificial Intelligence -Quantum computer can learn from experience.It can self correct and even modify the program code.The machine learning ability of quantum computer help to do things faster and efficiently. It can used for artificial intelligence experiments.NQAIL(New Quantum Artificial Intelligence Lab) at NASA's Ames research centre in silicon valley will be operated by NASA, Google and USRA. Google and NASA use the quantum computer for developing more advancements in Artificial Intelligence.