Quantum Information Science II, Part 2 - Efficient Quantum Computing - fault tolerance and complexity

• Efficient quantum computing - codes and fault tolerance
• Fault-tolerant quantum computation - introduction
• Computational capacity - communication over noisy wires
• Computational capacity - computation with noisy gates
• The threshold theorem - statement
• The threshold theorem - proof sketch - level 1
• Thresholds for reliable classical computation
• Principles of fault tolerance
• Examples of fault-tolerant and non-fault-tolerant procedures
• The circuit size of fault-tolerant procedures
• Threshold for quantum computation - fault-tolerant quantum procedures
• Fault-tolerant quantum gates on 5-qubit and 7-qubit codes
• Fault-tolerant quantum measurement of error syndromes
• Crude estimate of the threshold for reliable quantum computation
• Fault-tolerant quantum computation - theorem overview
• Fault-tolerant quantum computation - theorem idea
• Fault-tolerant quantum circuit construction example
• Fault-tolerant quantum computation - ingredients I
• The role of classical error correction in FTQC - measurement
• Fault-tolerant measurements - scheme with error
• Fault-tolerant quantum computation - ingredients II
• Fault-tolerant recovery from error - non-demolition measurement
• Fault-tolerant recovery from error - DiVincenzo-Shor method
• Fault-tolerant recovery from error - Steane method
• Beyond Clifford gates - the Gottesman-Chuang hierarchy