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Introduction to Quantum Error Correction E. Knill, R. Laflamme, A. Ashikhmin, H. Barnum, L. Viola and W. Zurek
 

Summary: Introduction to Quantum Error Correction
E. Knill, R. Laflamme, A. Ashikhmin, H. Barnum, L. Viola and W. Zurek
December 16, 2001
Contents
1 Concepts and Examples 4
1.1 Trivial Two-Bit Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 The Repetition Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 A Code for a Cyclic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Principles of Noise Control 10
2.1 Error Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 From Error Detection to Error Correction . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Quantum Error Correction 13
3.1 Trivial Two-Qubit Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Quantum Repetition Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 Quantum Code for a Cyclic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 Three Quantum Spin-Half Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 Error Models 22
4.1 The Standard Error Models for Qubits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2 Quantum Noise Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
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Source: Ashikhmin, Alexei - Enabling Computing Technologies, Bell Laboratories

 

Collections: Engineering; Mathematics; Computer Technologies and Information Sciences