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Analysis of quantum error-correcting...

Harrington, James William.

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Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes./
Author:	Harrington, James William.
Description:	197 p.
Notes:	Source: Dissertation Abstracts International, Volume: 65-10, Section: B, page: 5186.
Contained By:	Dissertation Abstracts International65-10B.
Subject:	Physics, General. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3151362
ISBN:	0496113860

Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes.
Harrington, James William.

Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes. - 197 p.

Source: Dissertation Abstracts International, Volume: 65-10, Section: B, page: 5186.

Thesis (Ph.D.)--California Institute of Technology, 2004.

Quantum information theory is concerned with identifying how quantum mechanical resources (such as entangled quantum states) can be utilized for a number of information processing tasks, including data storage, computation, communication, and cryptography. Efficient quantum algorithms and protocols have been developed for performing some tasks (e.g. , factoring large numbers, securely communicating over a public channel, and simulating quantum mechanical systems) that appear to be very difficult with just classical resources. In addition to identifying the separation between classical and quantum computational power, much of the theoretical focus in this field over the last decade has been concerned with finding novel ways of encoding quantum information that are robust against errors, which is an important step toward building practical quantum information processing devices.

ISBN: 0496113860Subjects--Topical Terms:

1018488
Physics, General.

Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes.
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100 1 $a Harrington, James William. $3 1903299
245 1 0 $a Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes.
300 $a 197 p.
500 $a Source: Dissertation Abstracts International, Volume: 65-10, Section: B, page: 5186.
500 $a Adviser: John Preskill.
502 $a Thesis (Ph.D.)--California Institute of Technology, 2004.
520 $a Quantum information theory is concerned with identifying how quantum mechanical resources (such as entangled quantum states) can be utilized for a number of information processing tasks, including data storage, computation, communication, and cryptography. Efficient quantum algorithms and protocols have been developed for performing some tasks (e.g. , factoring large numbers, securely communicating over a public channel, and simulating quantum mechanical systems) that appear to be very difficult with just classical resources. In addition to identifying the separation between classical and quantum computational power, much of the theoretical focus in this field over the last decade has been concerned with finding novel ways of encoding quantum information that are robust against errors, which is an important step toward building practical quantum information processing devices.
520 $a In this thesis I present some results on the quantum error-correcting properties of oscillator codes (also described as symplectic lattice codes) and toric codes. Any harmonic oscillator system (such as a mode of light) can be encoded with quantum information via symplectic lattice codes that are robust against shifts in the system's continuous quantum variables. I show the existence of lattice codes whose achievable rates match the one-shot coherent information over the Gaussian quantum channel. Also, I construct a family of symplectic self-dual lattices and search for optimal encodings of quantum information distributed between several oscillators.
520 $a Toric codes provide encodings of quantum information into two-dimensional spin lattices that are robust against local clusters of errors and which require only local quantum operations for error correction. Numerical simulations of this system under various error models provide a calculation of the accuracy threshold for quantum memory using toric codes, which can be related to phase transitions in certain condensed matter models. I also present a local classical processing scheme for correcting errors on toric codes, which demonstrates that quantum information can be maintained in two dimensions by purely local (quantum and classical) resources.
590 $a School code: 0037.
650 4 $a Physics, General. $3 1018488
690 $a 0605
710 2 0 $a California Institute of Technology. $3 726902
773 0 $t Dissertation Abstracts International $g 65-10B.
790 1 0 $a Preskill, John, $e advisor
790 $a 0037
791 $a Ph.D.
792 $a 2004
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3151362