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 Mar 27, 2007
Speaker(s): 

Universality of Fibonacci anyons, operator quantum error correction, Bacon-Shor codes

 

Tuesday Mar 27, 2007
Speaker(s): 

Non-Abelian anyons (charges, fusion rules, F and R matrices, pentagon and hexagon equations), Fibonacci anyons

 

Tuesday Mar 20, 2007
Speaker(s): 

Behavior of particles in qudit toric code, braid group, basic idea of fault tolerance with non-Abelian anyons

 

Tuesday Mar 20, 2007
Speaker(s): 

Toric code (definition, fault-tolerance, particle model of errors), definition of qudit toric code

 

Tuesday Mar 13, 2007
Speaker(s): 

One- and two-way quantum capacities for the erasure channel, upper and lower bounds on the quantum capacities for the depolarizing channel, coherent information

 

Tuesday Mar 13, 2007
Speaker(s): 

One- and two-way entanglement distillation protocols, twirling, stabilizer EDPs, definition of quantum channel capacity

 

Tuesday Mar 06, 2007
Speaker(s): 

Error assumptions for fault tolerance re-examined (Other error models, correlated errors, leakage errors, coherent and non-Markovian errors)

 

Tuesday Mar 06, 2007
Speaker(s): 

Circuit assumptions for fault tolerance re-examined (other universal gate sets, local gates, fresh ancillas, no measurements, parallelism)

 

Tuesday Feb 27, 2007
Speaker(s): 

Equivalence of fault-tolerant circuit to less noisy unencoded circuits, threshold theorem, calculation of the threshold.

 

Tuesday Feb 27, 2007
Speaker(s): 

Assumptions for fault tolerance, extended rectangles, good, bad, and correct rectangles.

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