Quantum Computing. Hafiz Md. Hasan Babu

they had generated a seven-qubit quantum computer. However, many researchers are skeptical about extending magnetic techniques much beyond 10 to 15 qubits because of diminishing consistency among the elements.

      Quantum computers established on semiconductor technology are yet another opportunity. In a collective approach, a discrete number of free electrons (qubits) reside within incredibly small sections known as quantum dots. Although relying on decoherence, such quantum computers are constructed on well-established, solid-state procedures and offer the prospect of readily applying integrated circuit ‘scaling’ technology. In addition, large groups of identical quantum dots could theoretically be contrived on a single silicon chip. The chip controls an external magnetic field that controls the electron spin states, while neighboring electrons are weakly coupled through quantum mechanical effects. An array of covered wire electrodes allows individual quantum dots, which have been discussed.

1.5 The working principles of quantum computers

      The huge amount of processing power created by computer designers has not yet been able to satisfy the desire for speed and computing ability. In 1947, Howard Aiken claimed that only six electronic digital computers would satisfy the computing needs of the United States. Others have made similar inaccurate predictions about the amount of computing power that would satisfy the ever-increasing needs of technology. Of course, Aiken did not take into account the large amounts of data produced by scientific research, the explosion of personal computers, or the appearance of the Internet, which have further driven the need for computing power.

      Scientists have already constructed basic quantum computers that can carry out certain calculations. Quantum computers will harness the power of atoms and molecules to achieve memory and processing activities. Quantum computers have the potential to achieve certain controls significantly faster than any silicon-based computer. In this book, the reader will learn the design mechanisms of a quantum computer and just how they will be adapted for the next era of computing.

      It is not necessary to go back too far to find the origins of quantum computing, as it was first conceived of less than 30 years ago. On the other hand, classical computers have been used, with many difficulties, for a comparatively long time. Paul Benioff is credited with being the first to apply quantum theory to computers, in 1981, when he posited creating a quantum Turing machine.

1.6 The evolution of quantum computers

      Quantum computing is still in its emerging stages. There is a long way to go before a usably running quantum computer can be built, let alone brought to the market. However, progress in this new technology is occurring regularly and no chronological record can ever be complete. What follows is a brief timeline clarifying key areas of progress in quantum computing. Much of the technical development has been achieved in this century while most of the primary theoretical perspectives were laid down in the late twentieth century.

      In 1980, Paul Benioff was the first to design a computer which operated under quantum mechanical principles. His idea of a quantum computer was based on Alan Turing’s famous paper tape computer, described in his article published in 1936. In 1981, Feynman proved that it was impossible to simulate quantum systems on a classical computer. His argument hinged on Bell’s theorem, written in 1964. In 1985, David Deutsch published a report describing the world’s first universal quantum computer. He showed how such a quantum machine could reproduce any realizable physical system. Enthusiasm for creating the first quantum computer was stimulated by Peter Shor’s algorithm in 1994. Shor described a method for factorizing large integers. This had serious implications for cryptography, which relies on this operation being difficult in order to keep codes secure. Shor’s algorithm searched for periodicities in long integer-sequences of repeated digits. It used the quantum principles of superposition to scour for periodicities in the astonishingly fast time of a few minutes. To perform this same computation on a classical computer would take longer than the age of the Universe. In 1996, Lov Grover used quantum mechanics to solve an old unstructured search problem. For example, if someone wants to match a large database of names with a long list of telephone numbers, a classical computer could only solve this problem by querying each name with a telephone number until it found the right one, which is not fewer than O(N) evalutions of the function. Grover’s quantum algorithm, however, produces the output value using only O(N) evaluations of the function.

      In 2000, the first working five-qubit nuclear magnetic resonance (NMR) computer was put through its paces at the Technical University of Munich. Shortly after, the Los Alamos National Laboratory surpassed this feat with a working seven-qubit NMR quantum computer.

      The year 2001 is known for the demonstration of Shor’s algorithm. A team at the IBM Almaden Research Center in California succeeded in factorizing the integer 15 into 5 and 3. They used a thimbleful of a bespoke liquid containing billions of molecules. The molecules were constructed from five fluoride and two carbon atoms, each with their own nuclear spin state. The molecules worked as a seven-qubit quantum computer when pulsed with electromagnetic waves and monitored using NMR.

      In 2006 researchers offered a new functioning standard by monitoring a 12-qubit quantum system with only minimal decoherence. NMR quantum information processors were used to decrypt the computation. These quantum controls led to the hope that higher-qubit quantum computers might be available one day. The same year, scientists took a step closer to the building of a quantum gate, the quantum representation of a mathematical rule. Also in 2006, scholars created molecules of quantum-dot pairs. These have great potential for quantum computers, in particular if more complex elements can be created.

      This book focuses on how quantum gates and quantum representations of different circuits are to be designed to make a complete quantum computer. Readers will be motivated to design such circuits and to make quantum representations of different sequential and logical circuits of their own with different examples and designs of the circuit.

1.7 Why pursue quantum computing?

      Despite the most remarkable wave of technological inventions, there are definite computational problems that the digital revolution still cannot seem to solve, even though some of these computational problems could be solved by scientific advances. Although conventional computers have doubled in processing speed and power nearly every two years for decades, they still do not appear to be fast eough to solve these enduring problems. In the long run, to solve the world’s most tenacious computing problems competently, we will have to turn to an utterly new and more capable machine: the quantum computer.

      Finally, the dissimilarity between a classical computer and a quantum computer is not like the difference between an old car and a new one. Instead, it is like the difference between a horse and a hawk: while one can run, the other can fly. Classical computers and quantum computers certainly have that difference. In this chapter we have taken a careful look at where the key differences lie and have taken a profound plunge into what makes quantum computers unique.

1.8 Summary

      This chapter mainly introduces researchers to quantum logic and simply delineates why future generations will choose quantum computing instead of conventional computers. In this chapter, the relation between reversible and quantum logic, the salient principles of quantum computers, their evolution, and necessity are briefly described.

Further reading

      [1] Bonsor K and Strickland J 2000 How quantum computers work How Stuff Works https://computer.howstuffworks.com/quantum-computer.htm (Accessed: 4 December 2018)

      [2] Wikipedia Quantum cellular automaton https://en.wikipedia.org/wiki/Quantum_cellular_automaton (Accessed: 4 December 2018)

      [3] Holton W C Quantum computer Encyclopædia Britannica https://www.britannica.com/technology/quantum-computer (Accessed: 4 December 2018)