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Studies on Entanglement in Nuclear and Electron Spin Systems for Quantum Computing

Robabeh Rahimi Darabad

Published Jan 1, 2006• 2 citations
OpenAlex

Abstract

The enormous impact of computers on everyday life is an incredible fact. The current technology of the computers is based on th technology of transistors, which is an appreciated synergy between computer science and quantum physics. Smaller transistors can work with less power, can be highly densed and can be switched on and off very fast. While the miniaturization is necessary to increase the computation power, this miniaturization also provides us with an intuitive way of understanding why, in a near future, quantum laws will become important for computation. Gordon Moore? in 1965 codified his law, known as Moore’s law, on the growth of computers. It states that the power of computers will double for constant cost roughly once every two years. This statement amazingly has come true for decades, since the 1960s. This growth is achieved through miniaturizing the size of the computers, by compacting the number of transistors. There is of course a limit for the number of transistors per chip and at present time it is almost 10 18 for a typical size of circuit components to be of the order of 100 nanometers. Then this is a fact that around 2020 we will reach the atomic size for storing a single bit of information, hence quantum effects

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The enormous impact of computers on everyday life is an incredible fact. The current technology of the computers is based on th technology of transistors, which is an appreciated synergy between computer science and quantum physics. Smaller transistors can work with less power, can be highly densed and can be switched on and off very fast. While the miniaturization is necessary to increase the computation power, this miniaturization also provides us with an intuitive way of understanding why, in a near future, quantum laws will become important for computation. Gordon Moore? in 1965 codified his law, known as Moore’s law, on the growth of computers. It states that the power of computers will double for constant cost roughly once every two years. This statement amazingly has come true for decades, since the 1960s. This growth is achieved through miniaturizing the size of the computers, by compacting the number of transistors. There is of course a limit for the number of transistors per chip and at present time it is almost 10 18 for a typical size of circuit components to be of the order of 100 nanometers. Then this is a fact that around 2020 we will reach the atomic size for storing a single bit of information, hence quantum effects
Q uantum mechanics has had an enormous technological and societal impact.To grasp this point, it is sufficient to cite the invention of the transistor, perhaps the most remarkable among the countless other applications of quantum mechanics.It is also easy to see the enormous impact of computers on everyday life.The importance of computers is such that it is appropriate to say that we are now living in the information age.This information revolution became possible thanks to the invention of the tran sistor, that is, thanks to the synergy between computer science and quantum physics.Today this synergy offers completely new opportunities and promises exciting advances in both funda mental science and technological application.We are referring here to the fact that quantum mechanics can be used to process and transmit information [1,2].Miniaturization provides us with an intuitive way of under standing why, in the near future, quantum laws will become important for computation.The electronics industry for com puters grows hand-in-hand with the decrease in size of integrated circuits.This miniaturization is necessary to increase computa tional power, that is, the number of floating-point operations per second (flops) a computer can perform.In the 1950's, electronic computers based on vacuum-tube technology were capable of performing approximately 103 floating-point operations per second, while nowadays there exist supercomputers whose power is greater than lOteraflops (1013 flops).As we have remarked, this enormous growth of computational power has been made possi ble owing to progress in m in ia tu riz a tio n , w hich m ay be quantified empirically in Moore's law.This law is the result of a remarkable observation made by Gordon Moore in 1965: the number of transistors on a single integrated-circuit chip doubles approximately every 18 24 months.This exponential growth has not yet saturated and Moore's law is still valid.At the present time the limit is approximately 108 transistors per chip and the typical size of circuit components is of the order of 100 nanometres.Extrapolating Moore's law, one would estimate that around the year 2020 we shall reach the atomic size for storing a single bit of inform atio n .At th a t p o in t, q u a n tu m effects will becom e unavoidably dominant.One should be aware that, besides quantum effects, other fac tors could bring Moore's law to an end.In the first place, there are economic considerations.Indeed, the cost of building fabri cation facilities to m an u factu re chips has also increased exponentially with time.Nevertheless, it is important to under stand the ultimate limitations set by quantum mechanics.Even though we might overcome economic barriers by means of tech nological breakthroughs, quantum physics sets fundamental limitations on the size of the circuit components.The first ques tion under debate is whether it would be more convenient to push References
In the preceding chapter we established that a suitable set of quantum gates, complemented by quantum error correction, allows us to produce a desired multiqubit unitary transformation. This transformation is one of the three steps in a quantum computation; the others, of course, are the preparation of the qubits in their initial state and the measurement of them after the transformation has been implemented. A quantum computation is designed to solve a problem or class of problems. The power of quantum computers is that they can do this, at least for some problems, very much more efficiently and quickly than any conventional computer based on classical logic operations. If we can build a quantum computer then a number of important problems which are currently intractable will become solvable. The potential for greatly enhanced computational power is, in itself, reason enough to study quantum computers, but there is another. Moore’s law is the observation that the number of transistors on a chip doubles roughly every eighteen months. A simple corollary is that computer performance also doubles on the same timescale. Associated with this exponential improvement is a dramatic reduction in the size of individual components. If the pace is to be kept up then it is inevitable that quantum effects will become increasingly important and ultimately will limit the operation of the computer. In these circumstances it is sensible to consider the possibility of harnessing quantum effects to realize quantum information processors and computers. We start with a brief introduction to the theory of computer science, the principles of which underlie the operation of what we shall refer to as classical computers. These include all existing machines and any based on the manipulation of classical bits. The development of computer science owes much to Turing, who devised a simple but powerful model of a computing device: the Turing machine. It its most elementary form, this consists of four elements. (i) A tape for data storage, which acts as a memory. This tape has a sequence of spaces, each of which has on it one of a finite set of symbols. (ii) A processor, which controls the operations of the machine.
Computers have become an indispensible part of our life. Advancements in the field of technology have led to smaller and more compact computers, while their processing power has increased. However, with parts getting smaller and more compact, quantum physics are making things a bit problematic. Transistors act like switches, either allowing electrons to pass through or blocking their passage. Transistors are already almost as small as atoms. Electrons will eventually be able to transfer themselves to the other side of the blocked passage via a process called quantum tunneling, making transistors useless. Classical computers and the way it works stop making sense in the quantum realm. A possible solution to this problem could be quantum computers, which takes advantage of quantum principles to work. In this paper, an overview of quantum computers, their working principles and the basics of the math behind such computers have been discussed. The future scope of such a computer, problems associated with implementing it as well as the problems to be dealt with in case a scalable quantum computer is built is also provided.
Over the past half century wires and logic gates in computers have halved in size every year and a half, creating a phenomenon known as the Moore’s law. As the size of computer components reduces towards the atomic scale, however, the classical laws of thermodynamics are no longer able to predict the real behavior of electronic devices. In this context, the theory of quantum mechanics becomes increasingly important to characterize how circuits operate. Quantum information is the theory of communication and computation born to study the potential arising from information encoded in elementary particles, such as photons. The essential goal of quantum information is to determine how the quantum laws ruling the peculiar phenomena happening at an atomic scale can be used to enhance the capabilities of computers and communication systems.
Computers today become faster by becoming smaller. By reducing the size of transistors, engineers are able to fit more of them on a given size microprocessor, thus increasing the processor's computational power. This process cannot continue forever. It has been estimated that sometime within the next two decades, at the current rate, engineers will be faced with the problem of building something that is smaller than an atom. This is as far as our current "classical" computing paradigm will take us. Quantum computing is a potential solution to this problem. This paradigm of computing seeks to directly exploit quantum mechanical phenomena to perform calculations or in some way boost computational efficiency. Some problems can theoretically be solved on a quantum computer exponentially faster than on a classical computer. An overview of the subject is provided here with emphasis on quantum information processing and physical realizations of a quantum computer. Included is a brief history of the subject, a discussion of quantum computing notions such as parallelism and entanglement and their use in quantum algorithms, and conjecture on the prospects and pitfalls of this theory.