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8.371

Quantum Information Science

3-0-9 units · Graduate

Examines quantum computation and quantum information. Topics include quantum circuits, the quantum Fourier transform and search algorithms, the quantum operations formalism, quantum error correction, Calderbank-Shor-Steane and stabilizer codes, fault tolerant quantum computation, quantum data compression, quantum entanglement, capacity of quantum channels, and quantum cryptography and the proof of its security. Prior knowledge of quantum mechanics required.

Spring 2006

Topics

  • Quantum Operations; Operator Sum Representation; System-Environment Model
  • Quantum Error Correction - Criteria and Examples
  • Calderbank Shor Steane Codes
  • Stabilizers; Stabilizer Quantum Codes
  • Topological Quantum Codes; Kitaev’s Anyon Model
  • Stabilizers II; Computing on Quantum Codes
  • Concatenated Codes; The Threshold Theorem
  • Cluster State Quantum Computation
  • Measurement and Teleportation Based Quantum Computation
  • Adiabatic Quantum Computation
  • Quantum Algorithms on Graphs; Quantum Random Walks
  • Quantum Algorithms: The Abelian Hidden Subgroup Problem; QFT Over Sn
  • The Nonabelian HSP; Hidden Dihedral Group; Positive and Negative Results
  • Channels I: Quantum Data Compression; Entanglement Concentration; Typical Subspaces
  • Channels II: Holevo’s Theorem; HSW Theorem; Entanglement Assisted Channel Capacity
  • Channels III: Quantum-Quantum Channels, Mother/Father Protocol; Distillable Entanglement
  • Entanglement as a Physical Resource
  • Quantum Protocols - Quantum Communication Complexity; Distributed Algorithms
  • Quantum Games
  • Quantum Cryptography

Readings

  • Nielsen, Michael A., and Isaac L. Chuang. Quantum Computation and Quantum Information . Cambridge, UK: Cambridge University Press, 2000. ISBN: 9780521635035.
    Listed reading

Prerequisites & course information

Same subject as 6.6420J, 18.436[J] Prereq: 18.435[J] G (Spring) 3-0-9 units

Sources