An introduction to Quantum Computing

The field of quantum information processing has made numerous promising advancements since its conception, including the building of two- and three-qubit quantum computers capable of some simple arithmetic and data sorting.  However, a few potentially large obstacles still > remain that prevent us from "just building one," or more precisely, building > a quantum computer that can rival today's modern digital computer. >   Among these difficulties, error correction, decoherence, and hardware architecture > are probably the most formidable.  Error correction is rather self > explanatory, but what errors need correction?  The answer is primarily > those errors that arise as a direct result of > decoherence > , > or the tendency of a quantum computer to decay from a given quantum state > into an incoherent state as it interacts, or entangles, with the state > of the environment.  These interactions between the environment and > qubits are unavoidable, and induce the breakdown of information stored > in the quantum computer, and thus errors in computation.  Before any > quantum computer will be capable of solving hard problems, research must > devise a way to maintain decoherence and other potential sources of error > at an acceptable level. >  Thanks to the theory (and now reality) of quantum error correction, first proposed in 1995 and continually developed since, small scale quantum computers have been built and the prospects of large quantum computers are looking up.  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.  In 1998, researches at Los Alamos National Laboratory and MIT led by Raymond Laflamme managed to spread a single bit of quantum information (qubit) across three nuclear spins in each molecule of a liquid solution of alanine or trichloroethylene molecules.  They accomplished this using the techniques of nuclear magnetic resonance (NMR).  This experiment is significant because spreading out the information actually made it harder to corrupt.  Quantum mechanics tells us that directly measuring the state of a qubit invariably destroys the superposition of states in which it exists, forcing it to become either a 0 or 1.  The technique of spreading out the information allows researchers to utilize the property of entanglement to study the interactions between states as an indirect method for analyzing the quantum information.  Rather than a direct measurement, the group compared the spins to see if any new differences arose between them without learning the information itself.  This technique gave them the ability to detect and fix errors in a qubit's phase coherence, and thus maintain a higher level of coherence in the quantum system.  This milestone has provided argument against skeptics, and hope for believers.  Currently, research in quantum error correction continues with groups at Caltech (Preskill, Kimble), Microsoft, Los Alamos, and elsewhere.

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At present, quantum computers and quantum information technology remains in its pioneering stage.  At this very moment obstacles are being surmounted that will provide the knowledge needed to thrust quantum computers up to their rightful position as the fastest computational machines in existence.  Error correction has made promising progress to date, nearing a point now where we may have the tools required to build a computer robust enough to adequately withstand the effects of decoherence.  Quantum hardware, on the other hand, remains an emerging field, but the work done thus far suggests that it will only be a matter time before we have devices large enough to test Shor's and other quantum algorithms.  Thereby, quantum computers will emerge as the superior computational devices at the very least, and perhaps one day make today's modern computer obsolete.   Quantum computation has its origins in highly specialized fields of theoretical physics, but its future undoubtedly lies in the profound effect it will have on the lives of all mankind.

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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. 

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