Behold your computer. Your computer represents the culmination of years of technological advancements beginning with the early ideas of Charles Babbage (1791-1871) and eventual creation of the first computer by German engineer Konrad Zuse in 1941. Surprisingly however, the high speed modern computer sitting in front of you is fundamentally no different from its gargantuan 30 ton ancestors, which were equipped with some 18000 vacuum tubes and 500 miles of wiring! Although computers have become more compact and considerably faster in performing their task, the task remains the same: to manipulate and interpret an encoding of binary bits into a useful computational result. A bit is a fundamental unit of information, classically represented as a 0 or 1 in your digital computer. Each classical bit is physically realized through a macroscopic physical system, such as the magnetization on a hard disk or the charge on a capacitor. A document, for example, comprised of n-characters stored on the hard drive of a typical computer is accordingly described by a string of 8n zeros and ones. Herein lies a key difference between your classical computer and a quantum computer. Where a classical computer obeys the well understood laws of classical physics, a quantum computer is a device that harnesses physical phenomenon unique to quantum mechanics (especially quantum interference) to realize a fundamentally new mode of information processing. In a quantum computer, the fundamental unit of information (called a quantum bit or qubit), is not binary but rather more quaternary in nature. This qubit property arises as a direct consequence of its adherence to the laws of quantum mechanics which differ radically from the laws of classical physics. A qubit can exist not only in a state corresponding to the logical state 0 or 1 as in a classical bit, but also in states corresponding to a blend or superposition of these classical states. In other words, a qubit can exist as a zero, a one, or simultaneously as both 0 and 1, with a numerical coefficient representing the probability for each state. This may seem counterintuitive because everyday phenomenon are governed by classical physics, not quantum mechanics – which takes over at the atomic level. This rather difficult concept is perhaps best explained through an experiment. Consider Figure 1 below:
Behold your computer. Your computer represents the culmination of years of technological advancements beginning with the early ideas of Charles Babbage (1791-1871) and eventual creation of the first computer by German engineer Konrad Zuse in 1941. Surprisingly however, the high speed modern computer sitting in front of you is fundamentally no different from its gargantuan 30 ton ancestors, which were equipped with some 18000 vacuum tubes and 500 miles of wiring! Although computers have become more compact and considerably faster in performing their task, the task remains the same: to manipulate and interpret an encoding of binary bits into a useful computational result. A bit is a fundamental unit of information, classically represented as a 0 or 1 in your digital computer. Each classical bit is physically realized through a macroscopic physical system, such as the magnetization on a hard disk or the charge on a capacitor. A document, for example, comprised of n-characters stored on the hard drive of a typical computer is accordingly described by a string of 8n zeros and ones. Herein lies a key difference between your classical computer and a quantum computer. Where a classical computer obeys the well understood laws of classical physics, a quantum computer is a device that harnesses physical phenomenon unique to quantum mechanics (especially quantum interference) to realize a fundamentally new mode of information processing. In a quantum computer, the fundamental unit of information (called a quantum bit or qubit), is not binary but rather more quaternary in nature. This qubit property arises as a direct consequence of its adherence to the laws of quantum mechanics which differ radically from the laws of classical physics. A qubit can exist not only in a state corresponding to the logical state 0 or 1 as in a classical bit, but also in states corresponding to a blend or superposition of these classical states. In other words, a qubit can exist as a zero, a one, or simultaneously as both 0 and 1, with a numerical coefficient representing the probability for each state. This may seem counterintuitive because everyday phenomenon are governed by classical physics, not quantum mechanics – which takes over at the atomic level. This rather difficult concept is perhaps best explained through an experiment. Consider Figure 1 below:
Quantum mechanics is one of the cornerstones of modern physics. It governs the behavior and the properties of matter in a fundamental way, in particular on the microscopic scale of atoms and molecules. Hence, what we may call a classical computer, i.e., those machines on or under the desktops in our offices together with all their potential descendants, are themselves following the rules of quantum mechanics. However, they are no quantum computers in the sense that all the inside information processing can perfectly be described within classical information theory. In fact, we do not need quantum mechanics in order to explain how the zeros and ones – the bits – inside a classical computer evolve. The reason for this is that the architecture of classical computers does not make use of one of the most fundamental features of quantum mechanics, namely the possibility of superpositions. Throughout the entire processing of any program on a classical computer, each of the involved bits takes on either the value zero or one. Quantum mechanics, however, would in addition allow superpositions of zeros one ones, that is bits – now called qubits (quantum-bits) – which are somehow in the state zero and one at the
In the twentieth century, quantum physics is one of the most successful approaches in scientific progress. To theorize the concept of quantum computing Max Planck's idea of the existence of energy in individual units like matter was used. Since then, the idea of manufacturing quantum computers for everyday use is becoming more plausible with technological advances in quantum theory. A classical computer carries out logical operations using a bit which is either 1 or 0. In contrast to a classical computer, a quantum computer works with a quantum bit or qubit, which is not limited to two states only. Qubits can exist in a superposition of the two states creating parallelism. Qubit represents the state of atoms, ions, photons or electrons. These qubits which work together with a control device act as a computer memory.Quantum computers have the potential to become million times more potent than present-day supercomputers due to the presence of these multiple states simultaneously. Concepts and ideas of quantum computing have been demonstrated by different methods like Ion Trap, Quantum Dot methods etc. However, the actual realization of such a superior system is still in the future. A strategy must be formulated to maintain decoherence and other potential sources of error at a permissible level.Astonishingly, quantum computing took a long time to take off, even though the physicists have known about the world of subatomic particles. Even so, it took computer scientists another half-century to consider harnessing quantum effects for computation. Also, it was later discovered that quantum computers could solve quantum mechanical many-body problems that are impractical to solve on a classical computer. The foundations of the subject of quantum computation may have become well-published, but the knowledge is still growing. Hence here is a research paper based on the study of quantum computation.
Today's computers work on bits that exist as either 0 or 1. Quantum computers aren't limited to two states; they encode information as quantum bits, or qubits, which can exist in superposition. Qubits represent atoms, ions, photons or electrons and their respective control devices that are working together to act as computer memory and a processor. Because a quantum computer can contain these multiple states simultaneously, it has the potential to be millions of times more powerful than today's most powerful supercomputers. A processor that can use registers of qubits will be able to perform calculations using all the possible values of the input registers simultaneously. This superposition causes a phenomenon called quantum parallelism, and is the motivating force behind the research being carried out in quantum computing. Due to technical obstacles, till date, a quantum computer has not yet been realized. But the concepts and ideas of quantum computing has been demonstrated using various methods like NMR, Ion Trap, Quantum Dot, Optical Methods, etc. A quantum computer manipulates qubits by executing a series of quantum gates, each a unitary transformation acting on a single qubit or pair of qubits. In applying these gates in succession, a quantum computer can perform a complicated unitary transformation to a set of qubits in some initial state. The qubits can then be measured, with this measurement serving as the final computational result. Research must devise a way to maintain decoherence and other potential sources of error at an acceptable level. Probably the most important idea in this field is the application of error correction in phase coherence as a means to extract information and reduce error in a quantum system without actually measuring that system. Thereby, quantum computers will emerge as the superior computational devices and perhaps one day make today's modern computer obsolete.
We have seen how information can be encoded onto a quantum system by selecting the state in which it is prepared. Retrieving the information is achieved by performing a measurement, and the optimal measurement in any given situation is usually a generalized measurement. In between preparation and measurement, the information resides in the quantum state of the system, which evolves in a manner determined by the Hamiltonian. The associated unitary transformation may usefully be viewed as quantum information processing; if we can engineer an appropriate Hamiltonian then we can use the quantum evolution to assist in performing computational tasks. Our objective in quantum information processing is to implement a desired unitary transformation. Typically this will mean coupling together a number, perhaps a large number, of qubits and thereby generating highly entangled states. It is fortunate, although by no means obvious, that we can realize any desired multiqubit unitary transformation as a product of a small selection of simple transformations and, moreover, that each of these need only act on a single qubit or on a pair of qubits. The situation is reminiscent of digital electronics, in which logic operations are decomposed into actions on a small number of bits. If we can realize and control a very large number of such operations in a single device then we have a computer. Similar control of a large number of qubits will constitute a quantum computer. It is the revolutionary potential of quantum computers, more than any other single factor, that has fuelled the recent explosion of interest in our subject. We shall examine the remarkable properties of quantum computers in the next chapter. In digital electronics, we represent bit values by voltages: the logical value 1 is a high voltage (typically +5 V) and 0 is the ground voltage (0 V). The voltage bits are coupled and manipulated by transistor-based devices, or gates. The simplest gates act on only one bit or combine two bits to generate a single new bit, the value of which is determined by the two input bits. For a single bit, with value 0 or 1, the only possible operations are the identity (which does not require a gate) and the bit flip.
As early as 1982 Richard P. Feynman suggested that it might be impossible to simulate quantum mechanical phenomena with a computer without an exponential slowdown the efficiency of computation. He also proposed that this problem may be avoided by allowing the computer to run according to the laws of quantum mechanics, thus implicitely suggesting that a computer based on the quantum mechanical systems, a quantum computer, might have exponentially more computational efficiency than any classical one. A quantum mechanical phenomenon that never occurs classical physics and which actually makes quantum computation interesting and powerful, is the superposition of states, which, loosely speaking, means that instead of being totally one single state, a particle can be in between many states. Compare this to the elements of classical computer, bits. A bit takes values zero or one, but never anything between. In a quantum computer, one is able to store it both values simultaneously one quantum bit, equally weighted or not. Moreover, the classical computer one can store a number from zero to 2n−1 a register of length n, whereas, quantum computation, all the values could be stored simultaneously. The computation, which is performed via unitary transformations the state vector space, then applies to all these values simultaneously. Thus the power of the quantum computation lies not the absolute speed of the hypothetetical quantum computer but the possibility to actually follow many computational path simultaneously, as a nondeterministic automaton does. Alas, the observation of the outcome will yield only one value destroying the rest irreversibly. However, using a procedure smart enough one could obtain some valuable information about the computation.