Quantum Computing Essay

Abstract

Envisage a computational system with memory exponentially greater than its size and capable of carrying out simultaneous calculations on a given set of inputs.  This system would be a quantum computer. Principles of quantum mechanics are necessary to make quantum computers a reality. Will such a computer be inevitable or hard to build?

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This paper analyses how quantum mechanics principles can be utilized to achieve increased computational power of computers. The challenge is solving complex problems which are exponential in nature such as factorization of large numbers using classical computers.  The concepts of classical computers such as data representation and storage are reviewed as a prelude to give an in-depth into their operation. These concepts are compared across classical and quantum computers and therefore drawing a model upon which quantum computers would be built. This paper concludes with an outlook to the prospects and feasibility of quantum computation in the future.

Introduction

A quantum computer is a devise that utilizes the concept of quantum mechanics to increase the computational power of computers above what is achievable by the classical computers (Jones, n.d). This idea arose as a result of scientists deliberations over the limits of information processing power of computers. According to Moore’s Law, continued technological developments would result into reducing sizes of computer chip circuitry to a point where the elements would be like atoms. This would create a problem because at the atomic point, the laws that govern the performance of the circuit would exploit the principles of quantum mechanical properties rather than classical properties. This brought the challenge of devising computers based on the fundamentals of quantum mechanics. In attempting to answer these concerns, Richard Feynman developed a model of computers based on quantum physics in 1982. In 1985, David Deutsch published a paper which suggested that the Feynman’s idea could be harnessed and modeled into realm of a quantum computer. Later in 1994, an algorithm was devised by Shor that was used to perform complex mathematical problems such as factorization in a quantum computer. This transformed quantum computing from a mere idea into an area of interest throughout the world (West, 2000).

Classical versus Quantum Computing

A classical computer relies on binary bits as the fundamental unit of representing information, which is digitally represented as a 0 or 1sometimes referred to as “on” or “off” in a classical computer. These bits are manipulated by Boolean algebra or logic such that they change state based on the algebra applied (Anissimov, 2003). This shows that the computer circuitry consisting of transistors and capacitors can only be in one state at a time. The speeds at which these states are switched from one to another are limited. As smaller circuitry continues to emerge, the threshold above which the classical laws of mechanics can go is reached beyond which the quantum laws of mechanics take over.

Quantum computers have different computational properties from the classical computers. In this case data is represented in a quantum bit also known as a qubit. This property is not binary but rather quaternary in nature and arises as a result of the quantum laws of mechanics. A qubit can exist either as a 0, a 1, or as the superposition of these states which gives it much more flexibility than the classical states. In a quantum computer, data is processed by bombarding the atom containing information with a beam of electrons or photons and their charge or polarization representing the qubit values of 0 or 1. Superposition and entanglement principles of quantum mechanics are the most relevant aspects in quantum computing (TechTarget, 2008).

Superposition

Consider a quantum bit as an electron or photon in a magnetic field, with the electron’s spin being either in phase with the field, a situation known as spin-up state or out of phase with the field, a situation known as spin-down state. The direction of the electron’s spin which represents the qubit states can be changed from one state to another by applying a laser beam in the magnetic field assuming that only one unit of the laser energy is applied. Halving the amount of laser energy applied isolates all external disturbances to the particles forcing the particles into a superposed state of both 0 and 1 according to the laws of quantum physics and therefore behaving as if in both states simultaneously. Each of the quantum bit used could acquire the superposition of both 0 and 1 state. A quantum computer is therefore capable performing 2n number of computations where n represents the number of qubits used. A quantum computer of 500 qubits would therefore perform 2500 computations in a single execution. This results into a massive parallelism which is not possible with classical computers. The question therefore arises of how these particles would interact with each other. These concerns would be answered by a concept called quantum entanglement (TechTarget, 2008).

Entanglement

 Particles in a magnetic field interact with each other such that the quantum states of the different interacting particles create a single entangled state. These entangled states are depended on one another so that the knowledge of spin state of one entangled electron whether up or down makes it possible for the spin state of the other entangled particle state which must be in the opposite direction to be known. From the concept of superposition, a particle is simultaneously in both spin up and spin down states and therefore measuring it entangles it to either of the states. According to Einstein phenomenon, the state of a particle is known at the time of measurement and the correlated particle assumes the opposite state (Thomas, n.d).

Quantum superposition and entanglement concepts yield a massive computational power. For example, taking a 2-bit register in a classical computer, only one of the four possible configurations 2n, where n=2 (00, 01, 10, 11) can be stored at a time. On the other hand, a 2-qubit register in a quantum computer is capable of storing all these configurations simultaneously. This storage capacity is exponentially increased with an increase in the number of qubits (TechTarget, 2008).

Challenges

Despite the numerous sound advancements in quantum computing, there still exist a number of challenges and obstacles. Interference, error correction and output observance are among the most common difficulties that quantum computation presents. During the computation of a quantum problem which is performed at a superposed state, any measurement causes the computation to collapse into a single state, a condition referred to as decoherence. For computations to give correct results, decoherence must be maintained as low as possible. Error correction arises as a result of interactions between qubits and the environment which causes the collapse of stored information resulting into errors into calculations. Output observance becomes difficult because retrieval of the output of a quantum computation might corrupt the data. For a 2500 quantum computation, there is only one chance between 1-2500 available options of observing the right output. A method to ensure that the observed value gives the desired output should be devised. This has been achieved by Grover’s algorithm which ensures that measurements results into a decoherence state which gives the correct answer (TechTarget, 2008).

Conclusion

There have been tremendous improvements in the field of quantum computing in the last decade despite the challenges and problems it has faced. Efforts to tackle these obstacles should be put in place to propel the enormous computational power of quantum computers into feasible reality. Great progress has been made concerning error correction with the development of error correction algorithms and with concerted efforts, a robust computer that is capable of withstanding decoherence would be built. This development would render the current classical computer obsolete and its future rests on how it would affect mankind (Leggett, 1999).

Reference:

Anissimov, M. (2003). What is a Quantum Computer? Retrieved March 1st, 2009,

from http://www.wisegeek.com/what-is-a-quantum-computer.htm

Jones, A.Z. (n.d). What Is a Quantum Computer? Retrieved March 1st, 2009, from

http://physics.about.com/od/quantumphysics/f/quantumcomp.htm

Leggett, T. (1999).Quantum theory: weird and wonderful. Retrieved March 1st, 2009,

from http://physicsworld.com/cws/article/print/856.

TechTarget (2008). Quantum Computing. Retrieved March 1st, 2009, from

http://whatis.techtarget.com/definition/0,,sid9_gci332254,00.html.

Thomas, A. (n.d). Quantum Entanglement. Retrieved March 1st, 2009, from

http://www.ipod.org.uk/reality/reality_entangled.asp.

West, J. (2000). The Quantum Computer. Retrieved March 1st, 2009, from

http://www.cs.rice.edu/~taha/teaching/05F/210/news/2005_09_16.htm