The idea of using quantum mechanics to provide more power than classical computers seem to have begun around 1981 to 1982, but Deutsch put the concept on a sounder footing a short time later. Deutsch reformulated the Turing thesis with the assertion that every finite realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means. However, he asserted that the output of a quantum machine, although fully determined by the input state, is not an observable itself. Progress beyond mathematical approaches came later when Lloyd suggested that arrays of weakly coupled quantum systems might be able to serve as the quantum computer if they were subjected to a sequence of controlled electromagnetic pulses, which could place the quantum bits into the desired super-positions. It was John von Neumann, working with the computer pioneers at the University of Pennsylvania, who suggested that the binary system should be used for simplicity in building computers.
The idea of using quantum mechanics to provide more power than classical computers seem to have begun around 1981 to 1982, but Deutsch put the concept on a sounder footing a short time later. Deutsch reformulated the Turing thesis with the assertion that every finite realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means. However, he asserted that the output of a quantum machine, although fully determined by the input state, is not an observable itself. Progress beyond mathematical approaches came later when Lloyd suggested that arrays of weakly coupled quantum systems might be able to serve as the quantum computer if they were subjected to a sequence of controlled electromagnetic pulses, which could place the quantum bits into the desired super-positions. It was John von Neumann, working with the computer pioneers at the University of Pennsylvania, who suggested that the binary system should be used for simplicity in building computers.
The idea of using quantum mechanics to provide more power than that available from classical computers seems to have begun around 1981–82 ( Benioff, 1982 ), but Deutsch (1985) put the concept on a sounder footing a short time later when he reformulated the Turing (1937) thesis with the assertion that every finite realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means. However, he asserted that the output of a quantum machine, although fully determined by the input state, is not an observable itself. Hence, the user must provide some cleverness if this state is to be determined. Benioff pointed out the need for the quantum state to experience interference, some indeterminism, and was what we would today call an entangled state. He also realized that non-dissipative evolution was unphysical, so immediately it became clear that a great deal of effort would be required to minimize the decoherence of the physical states. Deutsch (1989) then provided some input as to what type of states or systems might be usable in this process. Jozsa (1991) mathematically showed that one could associate a quantum state to each function that one desired to evaluate, and that this should lead to a rapid solution of problems via the quantum computer ( Deutsch and Jozsa, 1992 ). Since these introductions, the world has progressed rapidly into a determined search for applications of quantum mechanics throughout the information processing world.
Computation is a process of performing a large number of simple operations. The main building blocks of classical computers are bits. Each of them can take either the value 0 or 1. A series of gates can change these values by acting on them selectively. This process is structured to fulfil a purpose. For example, if we are interested in adding two numbers, the numbers are encoded into bits and gates are performed such that the final state of the bits reveals the desired answer: a number which is the sum of the initial ones. While it is possible to build algorithms that can perform almost any computation, it is also desirable to find the answer within a reasonable length of time or with a reasonable amount of resources. There is an ever-growing demand in computational power for both scientific and commercial purposes. Indeed, it is surprisingly easy to find an application that can jam even the fastest computer. This fuels a vast effort in the research of information science to increase the speed and processing power of computers. Modern computational models are based on the universal Turing machine (Turing, 1937). This is a theoretical information processing model that employs the elementary gate processes described above. It can efficiently simulate any other device capable of performing an algorithmic process. Since the introduction of the Turing machine, physics has influenced computation in many ways.
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.
Quantum computing is a prolific research area, halfway between physics and computer science [27, 29, 52]. Most likely, its origins may be dated back to 70's, when some works on quantum information began to appear (see, e.g., [34, 37]). In early 80's, R.P. Feynman suggested that the computational power of quantum mechanical processes might be beyond that of traditional computation models [25]. Almost at the same time, P. Benioff already proved that such processes are at least as powerful as Turing machines [9]. In 1985, D. Deutsch [22] proposed the notion of a quantum Turing machine as a physically realizable model for a quantum computer. From the point of view of structural complexity, E. Bernstein and U. Vazirani introduced in [20] the class BQP of problems solvable in polynomial time on quantum Turing machines, focusing attention on relations with the corresponding deterministic and probabilistic classes P and BPP, respectively. Several works in the literature explored classical issues in complexity theory from the quantum paradigm perspective (see, e.g., [7, 60, 61]).
Quantum computing stands as a pioneering field within computer science, leveraging the enigmatic principles of quantum mechanics to execute intricate calculations. At its heart lies the qubit, the elemental building block of quantum information, which resides in a state of superposition, representing both 0 and 1 concurrently. Quantum computers, constructed from assemblies of qubits, inhabit an expansive and intricate 2^n-dimensional complex Hilbert space, with their evolution governed by the Schrödinger equation. The process of quantum computation can be distilled into three key stages:1) Initialization of the input state: Initiating the quantum process; 2)Application of unitary transformations: Executing the desired transformations on the input state; 3) Measurement of the output state. Quantum computers serve as universal machines, capable of decomposing any unitary transformation into a sequence of fundamental gates. This chapter will reveal the importance of quantum mechanics, quantum computation and its applications.