Quantum Error Correction Course 2007

An in-depth introduction to quantum error correction, fault-tolerant quantum computing, and related topics. Covers stabilizer codes, CSS codes, higher-dimensional codes, specific code constructions, entanglement purification protocols, and quantum channel capacity. Also bounds on quantum error correction: quantum Hamming bound, quantum Singleton bound, linear programming bounds and the quantum MacWilliams identity; and principles of fault-tolerant quantum computation: fault-tolerant error measurement, fault-tolerant gate design, the threshold for fault-tolerant quantum computation, and topological fault-tolerance.

 

Tuesday Feb 20, 2007
Speaker(s): 

Fault-tolerant stabilizer state preparation, Steane error correction, universal fault-tolerant set of gates through gate teleportation, magic state distillation

 

Tuesday Feb 20, 2007
Speaker(s): 

Definition of fault tolerance, Shor error correction, fault-tolerant measurement for stabilizer and CSS codes

 

Tuesday Feb 13, 2007
Speaker(s): 

Transversal Pauli group, transversal Clifford group for 7-qubit code, transversal gates for 5-qubit code, overview of fault-tolerant protocols.

 

Tuesday Feb 13, 2007
Speaker(s): 

Examples of qudit stabilizer codes, polynomial codes, Clifford group for qudits, introduction to fault-tolerance, definition of transversal gates, definition of fault-tolerant gates

 

Tuesday Feb 06, 2007
Speaker(s): 

Weight enumerators, quantum MacWilliams identity, quantum shadow enumerator, higher-dimensional Pauli group, stabilizer codes for qudits

 

Tuesday Feb 06, 2007
Speaker(s): 

Generators of symplectic group, quantum Gilbert-Varshamov bound, quantum Hamming bound, quantum Singleton bound

 

Tuesday Jan 30, 2007
Speaker(s): 

Guest lecturer Robert Raussendorf: graph states

 

Tuesday Jan 30, 2007
Speaker(s): 

Guest lecturer Raymond Laflamme: experimental quantum error correction

 

Tuesday Jan 23, 2007
Speaker(s): 

Clifford group as symplectic group, generators of the Clifford group & encoding circuits for stabilizer codes, efficient simulation of Clifford group circuits, efficient simulation of Pauli measurements

 

Tuesday Jan 23, 2007
Speaker(s): 

Finite field GF(4), stabilizer codes as GF(4) codes, perfect quantum codes, definition of Clifford group, sample elements of Clifford group

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