Quantum Computation

Fall 2009

4042 Bren Hall

irani@ics.uci.edu

Bren Hall 1423

No class: Oct 15, 22, 27

Extra lecture: Tue, Dec 8, 10:30-12:30pm

- Introduction to quantum mechanics from the perspective of quantum information.
- Formal models of quantum computation and quantum complexity classes.
- Quantum algorithms: quantum fourier transform and applications (including Shor's algorithm for factoring), quantum search, quantum simulation.
- Limitations on quantum computation: lower bounds for search, the class QMA and hardness results for computing fundamental properties of quantum systems.
- Quantum entanglement, especially as it pertains to computational complexity.

- Kitaev, Shen and Vyalyi,
__Classical and Quantum Computation__ - Nielsen and Chuang,
__Quantum Computation and Quantum Information__ - Mermin,
__Quantum Computer Science__ - Umesh Vazirani's Course Notes on Quantum Computation: link.
- John Preskill's Course Notes on Quantum Computation: link .
- Scott Aaronson's Course Notes on Quantum Complexity Theory: link .
- Scott Aaronson's Course Notes on Quantum Computing Since Democritus: link .
- Qubits, Quantum Mechanics and Computers: Course Notes link .
- Andrew Child's course on Quantum Algorithms: link .

Date | Topic |
---|---|

Sep 24 | Quantum Mechanics Postulates, Qubits |

Sep 29 | Observables, Hamiltonian, Schrodinger's Eqn |

Oct 1 | Tensor products, Entanglement, Bell Inequalities |

Oct 6 | Quantum circuits, Universal gate sets |

Oct 8 | Quantum Complexity Classes, QFT over Z_2^N Deutsch-Jozsa |

Oct 13 | BQP in PSPACE, Simon's Algorithm |

Oct 20 | QFT over Z_N, Factoring reduces to Order Finding |

Oct 29 | Shor's Factoring Algorithm |

Nov 3 | Factoring Recap, Hidden Subgroup Problem |

Nov 5 | Phase Estimation, Discrete Log |

Nov 10 | Lower Bound for Unstructured Search |

Nov 12 | Grover Search, Quantum Simulation |

Nov 17 | Search by Quantum Walk |

Nov 19 | Quantum Hitting Time |

Nov 24 | Quantum Walk Algorithm for Search and Element Distinctness |

Dec 1 | Adiabatic Quantum Computation |

Dec 3 | QMA-completeness |

Dec 8 | Error Correcting Codes |