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	Quantum error correction - Wikipedia, the free encyclopedia
		Quantum error correction is for use in quantum computing to protect quantum information from errors due to decoherence and other quantum noise.
		Quantum error correction is essential for fault-tolerant quantum computation which is designed to deal not just with noise on stored quantum information, but also with faulty quantum gates, faulty quantum preparation, and faulty measurements.
		Although copying is not possible with quantum information, due to the no-cloning theorem, the information of one qubit may be spread onto several (physical) qubits by using a quantum error correcting code.
	en.wikipedia.org /wiki/Quantum_error_correction (713 words)

	Quantum Error Correction (Site not responding. Last check: 2007-11-04)
		During the correction procedure, the entanglement between the system and its environment is transferred to an entanglement between the measuring apparatus and the environment.
		Third, the probability of failure of the quantum error correction falls exponentially with the redundancy, in the limit of large redundancy, as long as the error rate is below a given level [4,5].
		The context of quantum computing is another matter, however, and it remains to be seen whether quantum error correction can be made sufficiently robust against noise during the correction process itself.
	cam.qubit.org /articles/intros/QEC.php (1370 words)

	Biological vs. quantum error correction mechanisms
		Error correction mechanisms are common in biology and widely thought of as endemic to that realm to the exclusion of the quantum.
		We would conclude that the error correction mechanisms found in biological organisms are pre-dated by their occurrence in quantum sources and the maintenance of error correction mechanisms in the machinery below the biological even permits them to function and to exist.
		We would say that error correction mechanisms cannot be used as an example of a life feature that shows a level of organization not found in the physical.
	www.mightymall.com /1st3seconds/errorcm.html (842 words)

	Quantum Consciousness
		Technological quantum computing schemes avoid decoherence because of low temperatures and the use of quantum error correction.
		Quantum error correction may be facilitated by topologies -- for instance, toroidal surfaces (e.g.
		Four vibrational patterns in the microtubule lattice (top), which correlate with functional attachment patterns of microtubule-associated proteins are the eigenstates of a quantum superposition of all fours states (bottom).
	www.quantumconsciousness.org /views/Topological.html (257 words)

	Quantum Error Correction for Phase Errors
		Currently envisaged scalable quantum computers require the use of quantum error correction to enable relatively error-free computation on a platform of physical systems that are inherently error-prone.
		Without errors between encoding and decoding, the output state should be the same as the input state, provided that the encoding and decoding procedures are implemented perfectly.
		The red curve is the fidelity of the output qubit before the final Toffoli gate that corrects the errors based on the syndrome.
	www.eskimo.com /~knill/qip/nmrprhtml/node15.html (837 words)

	Genetic Algorithms and Quantum Error Correction
		Quantum mechanical effects are only noticeable on the atomic scale, and as the system we study gets larger, the laws of quantum mechanics "simplify" into the laws of classical physics.
		A quantum computer is not even based on classical logic, but Quantum Logic and instead of classical bits (binary digits), they operate on Qubits (Quantum Bits - a quantum superposition of state vectors 1 and 0 and everything in between).
		A quantum computer would conceivably be an array of such quantum dots, where a qubit would be an entanglement of energy states within a dot.
	individual.utoronto.ca /rezalotun/qc (1602 words)

	[No title]
		Such type of error correction was considered impossible, since classical error correcting is done mostly by duplication, whereas the no-cloning theorem prevented such duplications.
		So quantum computation can be done, at least, in theory but though there are some major problems associated with the actual simulation of these computations physicists, mathematicians, computer scientists are willing to put a lot of effort into this field.
		Though quantum computation has shown a lot of promise, it must be noted that every classical problem may not have a quantum solution, even if it does, this does not mean that such a solution will always be preferred over the classical one.
	www.clarkson.edu /honors/research/summer_papers/Ganguly-Srabonti.doc (3230 words)

	The Quantum Pontiff » Ion Trap Milestone
		Quantum error correction protects information stored in two-level quantum systems (qubits) by rectifying errors with operations conditioned on the measurement outcomes.
		We verify error correction by comparing the corrected final state to the uncorrected state and to the initial state.
		In principle, the approach enables a quantum state to be maintained by means of repeated error correction, an important step towards scalable fault-tolerant quantum computation using trapped ions.
	dabacon.org /pontiff/index.php?p=746 (286 words)

	Quantum Error Correction
		I have also written a dissertation on quantum error correction, although that was in graduate school, so maybe mine was more technical than yours has to be.
		Gottesman's stabilizer formalism for quantum error correcting codes and its connection to classical error correction codes.
		Of course, whilst this is mathematically nice, it defeats the main point of quantum error correction, which is that it works for all states and all independednt error models.
	www.physicsforums.com /showthread.php?t=71355 (733 words)

	Quantum error correction for communication with linear optics (Site not responding. Last check: 2007-11-04)
		ABSTRACT: Quantum error correction for communication with linear optics Improving the signal-to-noise ratio in optical communication systems is a fundamental requirement for cost-effective data transmission.
		This is particularly important for the transmission of noise-intolerant quantum states: excess noise at the quantum level destroys the coherence of the states, rendering classical error correction or amplifier-based schemes useless for quantum communication.
		This quantum error-correction scheme may thus find application in quantum cryptographic networks (where low noise is equivalent to high security), possibly extending their range far beyond limits imposed by system losses.
	www.weizmann.ac.il /chemphys/schmuel/abstracts/bB98.html (205 words)

	Quantum Error Correction
		The principles of error correction outlined in Sec.
		The main difference is that the physical system to be used for representing and processing information behaves quantum mechanically and the type of information is quantum.
		We illustrate the principles of quantum error correction by considering quantum versions of the three examples of Sect.
	www.eskimo.com /~knill/qip/ecprhtml/node8.html (117 words)

	List of Conferences and Seminars
		Quantum trajectory techniques enable one to replace a Markovian master equation with a stochastic differential equation for a single quantum state in Hilbert space; as such, they are useful as quantum Monte Carlo techniques.
		The advantages and disadvantages of quantum trajectory simulations for quantum error correction are discussed, along with the results of simulations for simple and fault-tolerant correction algorithms, and the object-oriented code used to generate the results.
		The main difference between bulk quantum computation and the usual paradigm is that it uses an incoherent sum of quantum computers which cannot be accessed individually, both in the state preparation and in the readout process.
	qso.lanl.gov /qc/confsem.html (2340 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		An error correcting code with data redundancy that repeats the original information a number of times is also known as a repetition code.¡nZ;ª)^ó ¨Classical Linear Codes¨iA code that encodes k bits in n bits (n>k) is called an [n,k] code.
		Quantum errors are usually more severe and varied than their classical counterparts.
		Quantum registers require to be stable for relatively long periods of time, so computations can be performed or information transmitted to other systems.
	www.science.gmu.edu /~rgomez/jeff/qec.ppt (1475 words)

	Quantum Error Correction Project (Aotearoa)
		Quantum computing is a relatively new area that provides a way to progress to new levels of computational power using, not 17th century physics, but 20th century quantum mechanics.
		The principle aim of this project is to improve the understanding of the quantum error correction mechanism and to investigate and develop classes of quantum error correcting codes.
		In the near future it is predicted that quantum computers will be an integral part of modern society, speeding up the flow and analysis of information, eliminating or at least reducing the bottlenecks that certain kinds of “hard” problems cause.
	homepage.mac.com /dglynn/quan_index.htm (1567 words)

	QEC Project (Aotearoa)
		Quantum computing is a new area that provides a way to progress to new levels of computational power using, not 17th century physics, but 20th century quantum mechanics.
		A main block to its use is the inherent instability of quantum systems due to an effect called decoherence, which ties together different parts of the quantum world.
		It is predicted that quantum computers will be an integral part of future society, speeding up the flow and analysis of information, eliminating or at least reducing the bottlenecks that certain kinds of hard problems cause It has also been claimed that it will make information flow more secure.
	homepage.mac.com /dglynn (252 words)

	Quantum Error Correction (Site not responding. Last check: 2007-11-04)
		Express the 32 states of the system in a new basis where AX1 is X applied to the first bit of A, etc. Note that these 32 states are orthonormal.
		Finding a basis in which all possible error syndromes result in orthogonal states which can be separated by an appropriate Hamiltonian is the real trick of quantum error correction.
		which is the same state as the original, except that the error has been forced into randomizing the absolute phase of the output.
	members.aol.com /jmtsgibbs/qcode5.htm (392 words)

	Talk Abstract: Orthogonal Geometry and Quantum Error Correction (Site not responding. Last check: 2007-11-04)
		The unreasonable effectiveness of quantum computing is founded on coherent quantum superposition or entanglement which allows a large number of calculations to be performed simultaneously.
		In classical computing one can assemble computers that are much more reliable than any of their individual components by exploiting error correcting codes.
		In quantum computing this was thought to be precluded by the Heisenberg Uncertainty Principle as recently as 2 years ago.
	www.ima.umn.edu /cc/wkshp_abstracts/calderbank1.html (128 words)

	AMERICAN MATHEMATICAL MONTHLY - December 2001
		The limitations of current technology and some of the underlying principles of quantum mechanics make quantum computers much more error prone than classical ones, so it is necessary to detect and correct errors in mid-computation.
		Moreover, the “no-cloning principle” of quantum mechanics seems to preclude the benefits of redundancy for error correction.
		We begin with a brief primer of quantum theory and then describe qubit errors and the error group they generate.
	www.maa.org /pubs/monthly_dec01_toc.html (610 words)

	Quantum Error Correction (Site not responding. Last check: 2007-11-04)
		In the course of processing in a quantum computer the qubit may be in a superposition of 0 and 1:
		In this example we are not worried about phase errors, which this correction scheme is helpless against.
		In order to protect against both phase and flip errors five qubits must be sent for each qubit of message.
	www.members.aol.com /jmtsgibbs/qcode3.htm (542 words)

	Quantum Error Correction (Site not responding. Last check: 2007-11-04)
		the description of known quantum error-correcting codes and
		are given which map 3 qubits to 8 qubits correcting 1 error,
		errors, and 1 to 29 qubits correcting 5 errors.
	q-error.net.ru (62 words)

	Perfect quantum error correction coding in 24 laser pulses (Site not responding. Last check: 2007-11-04)
		An implementation of this coding circuit on an ion-trap quantum computer is described that requires 26 laser pulses.
		In addition, the performances of two error-correction schemes, one based on the quantum Zeno effect and the other using standard methods, are compared.
		The quantum Zeno error correction scheme is found to fail completely for a model of noise based on phase diffusion.
	www.weizmann.ac.il /chemphys/schmuel/abstracts/bs97.html (149 words)

	Physics News Update, Number 388
		Skeptics have maintained that quantum computers would crash before carrying out a useful calculation since the devices rely on fragile, easily corrupted quantum states.
		Proposed in 1995 and developed unceasingly since then, quantum error correction has been all theory up until now.
		With this technique, they were able to detect and fix errors in a bit's "phase coherence," the phase relationship between the quantum waves corresponding to the 0 and 1 states.(D.G. Cory et al., Physical Review Letters, 7 Sept 1998.)
	www.aip.org /enews/physnews/1998/physnews.388.htm (574 words)

	Quantum Computing References (Site not responding. Last check: 2007-11-04)
		Some references on quantum computing and error correction, provided by Harriet Pollatsek.
		Calderbank, Rains, Shor, and Sloane, "Quantum error correction and orthogonal geometry, " Phys.
		Gottesman, "Class of quantum error-correcting codes saturating the quantum Hamming bound," Phys.
	www.maths.qmw.ac.uk /~pjc/quantum.html (162 words)

	The Andrew Steane Group homepage
		, but which otherwise is stable (in particular, the precession is free of phase error).
		First, completely general error processes can be corrected, including relaxation and entanglement with the environment, and to do this it is sufficient merely to be able to correct for spin flips (s
		Cependant, en adaptant des méthodes classiques de correction d'erreur, l'information quantique peut être stabilisée activement.
	eve.physics.ox.ac.uk /Personal/steane/QEC.html (1372 words)

	Michael Nielsen » Blog Archive » New paper: Operator quantum error correction
		A new paper (postscript), joint with David Poulin, all about operator quantum error correction, a clever way (alas, not my idea!) of protecting quantum states against the effects of noise.
		This idea - that a quantum system can correct itself - is absolutely fascinating, and runs completely counter to the standard folk “wisdom” about quantum mechanics, namely that quantum states are delicate objects that are easily (and irreversibly) destroyed.
		This entry was posted on Thursday, June 9th, 2005 at 1:01 pm and is filed under General.
	www.qinfo.org /people/nielsen/blog/?p=235 (176 words)

	Talk Abstract: Orthogonal Geometry and Quantum Error Correction
		As the components of computer circuits become very small their description must be given by quantum mechanics.
		Today experimental physicists are demonstrating control over the kind of events where one or two atoms are manipulated with one or two photons.
		If we look back 25 years it was generally believed that private communication over a public channel was impossible unless the two parties had agreed beforehand on some random secret information noone else knew.
	www.ima.umn.edu /cc/wkshp_abstracts/calderbank/author.html (387 words)

	QiSci » Blog Archive » Generalized quantum error-correction (Site not responding. Last check: 2007-11-04)
		Standard quantum error-correction is based on the idea of putting the information to be protected (e.g., a qubit) into a subspace of a large Hilbert space (e.g., a 7-qubit space).
		Recent work has generalized this idea, allowing information to be stored in a subsystem of a subspace.
		In this talk, I’ll describe a theory of generalized quantum error-correction.
	www.qinfo.org /?p=124 (157 words)

	Realization of quantum error correction : Nature
		and communication require error control to protect quantum information against unavoidable noise.
		protects information stored in two-level quantum systems (qubits) by rectifying errors with operations conditioned on the measurement outcomes.
		Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins
	dx.doi.org /10.1038/nature03074 (330 words)

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