Error Correction: New Applications
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en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 18 Dec 2014 20:17:11 GMTThu, 18 Dec 2014 20:17:11 GMTNew applications in the Error Correction categoryhttp://www.mapleprimes.com/images/mapleapps.gifError Correction: New Applications
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Simulation of a five qubits convolutional code
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We describe in this work a five-qubit quantum convolutional error correcting code and its implementation on a classical computer. The encoding and decoding circuits and an error correction procedure are presented. We will verify that if any X, Y, Z error or any product of them occurs on one or two qubit, this correction always allows to recover the useful information or to obtain a list of possible errors. The originality in this correction is the winning time obtained by measuring only the required syndromes, thus avoiding the decoherence phenomenon. Also, we give the average fidelity for double errors recovered as single errors having same syndrome.<img src="/applications/images/app_image_blank_lg.jpg" alt="Simulation of a five qubits convolutional code" align="left"/>We describe in this work a five-qubit quantum convolutional error correcting code and its implementation on a classical computer. The encoding and decoding circuits and an error correction procedure are presented. We will verify that if any X, Y, Z error or any product of them occurs on one or two qubit, this correction always allows to recover the useful information or to obtain a list of possible errors. The originality in this correction is the winning time obtained by measuring only the required syndromes, thus avoiding the decoherence phenomenon. Also, we give the average fidelity for double errors recovered as single errors having same syndrome.142318Wed, 16 Jan 2013 05:00:00 ZFatiha MerazkaFatiha MerazkaSimulation on maple of the nine qubit Shor code using Feynman program
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<p><span id="ctl00_mainContent__documentViewer"><span><span class="body summary">
<p align="left">To simulate the evolution and behavior of an n-qubits system, a quantum simulator within the framework of the computer algebra system Maple called Feynman program has been built by S.Fritzsche and T.Radtke. In this work we use this program to implement the nine qubit Shor quantum error correcting code on a classical computer . We will present the encoding and decoding circuits and describe the error correction procedure using the Shor code gen-erators. We will verify that if any X, Y or Z error occur on any single qubit this correction procedure always allow to recover the usuful information. More-over, it permit at the end to put all the ancillas in the initial state and then too use them again. The simulation permit also the decoding without correction to measure all the output errors and know something about the canal transmitting the information.</p>
</span></span></span></p><img src="/view.aspx?si=34917//applications/images/app_image_blank_lg.jpg" alt="Simulation on maple of the nine qubit Shor code using Feynman program" align="left"/><p><span id="ctl00_mainContent__documentViewer"><span><span class="body summary">
<p align="left">To simulate the evolution and behavior of an n-qubits system, a quantum simulator within the framework of the computer algebra system Maple called Feynman program has been built by S.Fritzsche and T.Radtke. In this work we use this program to implement the nine qubit Shor quantum error correcting code on a classical computer . We will present the encoding and decoding circuits and describe the error correction procedure using the Shor code gen-erators. We will verify that if any X, Y or Z error occur on any single qubit this correction procedure always allow to recover the usuful information. More-over, it permit at the end to put all the ancillas in the initial state and then too use them again. The simulation permit also the decoding without correction to measure all the output errors and know something about the canal transmitting the information.</p>
</span></span></span></p>34917Sat, 05 Dec 2009 05:00:00 ZMOUZALI AZIZMOUZALI AZIZExtended (24, 12) Binary Golay Code: Encoding and Decoding Procedures
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It has been shown in the worksheet how to implement encoding and decoding of triple error correcting (24, 12) binary Golay code. The worksheet proves that Maple is an excellent (but underestimated) tool for teaching error-correcting codes.<img src="/view.aspx?si=1757/golay_2.gif" alt="Extended (24, 12) Binary Golay Code: Encoding and Decoding Procedures" align="left"/>It has been shown in the worksheet how to implement encoding and decoding of triple error correcting (24, 12) binary Golay code. The worksheet proves that Maple is an excellent (but underestimated) tool for teaching error-correcting codes.1757Fri, 30 Jun 2006 00:00:00 ZProf. Czeslaw KoscielnyProf. Czeslaw KoscielnyExploring self-dual codes with Maple
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This worksheet demonstrates the use of Maple for calculating results in exploring the algebraic properties of self-dual codes . It illustrates how computer algebra systems allow us understanding some complicated algebraic theories involved in the analysis of this type of codes avoiding the need for lengthy and tedious algebraic computations, and encouraging their more detailed comprehension.<img src="/view.aspx?si=3887//applications/images/app_image_blank_lg.jpg" alt="Exploring self-dual codes with Maple" align="left"/>This worksheet demonstrates the use of Maple for calculating results in exploring the algebraic properties of self-dual codes . It illustrates how computer algebra systems allow us understanding some complicated algebraic theories involved in the analysis of this type of codes avoiding the need for lengthy and tedious algebraic computations, and encouraging their more detailed comprehension.3887Wed, 20 Jun 2001 00:00:00 ZEdgar MartÌnez-MoroEdgar MartÌnez-MoroAccuracy of error correcting codes
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We have been looking at error correcting codes. The justification for using error correcting codes is that we want to improve the accuracy of transmission over a noisy communications channel. The question to be addressed in this worksheet is how much these codes improve the reliability of the channel.question arises. The broader background question is to determine the cheapest (most efficient) code that will provide the level of reliability we need. <img src="/view.aspx?si=3534//applications/images/app_image_blank_lg.jpg" alt="Accuracy of error correcting codes" align="left"/>We have been looking at error correcting codes. The justification for using error correcting codes is that we want to improve the accuracy of transmission over a noisy communications channel. The question to be addressed in this worksheet is how much these codes improve the reliability of the channel.question arises. The broader background question is to determine the cheapest (most efficient) code that will provide the level of reliability we need. 3534Mon, 18 Jun 2001 00:00:00 ZProf. Michael MayProf. Michael May