Quantum error correction
Farhat Mehemed Abdulhadi Zargoun;
Abstract
Communication is the prototypical application of error-correction methods. To communicate, a sender needs to convey information to a receiver over a "noisy communication channel". Such a channel can be thought of as a means of transmitting an information-carrying physical system from one place to another. During transmission, the physical system is subject to disturbances that can a ffcct the in formation carried. To usc a communication channeL the sender needs to "encode" the information to be transmitted in the physical system. After transmission, the receiver ..decodes" the information.
The principles of error correction apply to the quantum setting as readily as to the lassical setting. 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.
It has been proven that quantum in formation processing can he used to solve
problems in cryptography, secure communication and physics simulation exponentially faster than any of its conceivable classical analogues. There are numerous proposals for building quantum computers. Quantum data is very vulnerable to decoherance, interaction with the environment which is due to incomplete isolation of the system fi•om the rest of the world. Also. control errors, which arc caused by calibration errors and fluctuations in control parameters, have to be taken care of.
In a real quantum channel always some error occurs. J\n input state can be changed or even worse can be entangled with the environment. For correcting such errors we need to introduce some additional information which let us figure out what happened, the so called redundancy. In a transmission, often redundancy is encoded l'or several quhits together. For this purpose we need quantum error correction codes (QECC).
Soon after the existence of quantum error correction was proved in the pioneering paper by Shor, the first constructions of good quantum error correcting codes were given by Steanc, Caldcrbank and Shor. These codes
The principles of error correction apply to the quantum setting as readily as to the lassical setting. 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.
It has been proven that quantum in formation processing can he used to solve
problems in cryptography, secure communication and physics simulation exponentially faster than any of its conceivable classical analogues. There are numerous proposals for building quantum computers. Quantum data is very vulnerable to decoherance, interaction with the environment which is due to incomplete isolation of the system fi•om the rest of the world. Also. control errors, which arc caused by calibration errors and fluctuations in control parameters, have to be taken care of.
In a real quantum channel always some error occurs. J\n input state can be changed or even worse can be entangled with the environment. For correcting such errors we need to introduce some additional information which let us figure out what happened, the so called redundancy. In a transmission, often redundancy is encoded l'or several quhits together. For this purpose we need quantum error correction codes (QECC).
Soon after the existence of quantum error correction was proved in the pioneering paper by Shor, the first constructions of good quantum error correcting codes were given by Steanc, Caldcrbank and Shor. These codes
Other data
| Title | Quantum error correction | Other Titles | تصحيح الأخطاء الكمية | Authors | Farhat Mehemed Abdulhadi Zargoun | Issue Date | 2005 |
Attached Files
| File | Size | Format | |
|---|---|---|---|
| B13119.pdf | 967.25 kB | Adobe PDF | View/Open |
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