*Course Number*: CSC2451/MAT1751H

*Location*: Bahen 1220

*Date/Time*: Wednesday 2-5pm

*Office hours*: TBD

## Description

This course will give a broad overview of the field of quantum computing. We will start with a crash course in the fundamentals of quantum computing (qubits, quantum circuits, basic quantum algorithms such as Grover’s search algorithm and Shor’s factoring algorithm). Armed with the basics, we will then explore topics at the frontier of quantum computing: quantum simulation, quantum cryptography, connections with physics, quantum machine learning algorithms, and quantum supremacy. Students will make project presentations at the end of the course. This is a theoretical course that requires mathematical maturity and a strong background in linear algebra and probability theory.

## Schedule (*tentative*)

Date |
Topic, Notes, and References |
---|---|

September 12 | Administrativa. Basics of quantum information. |

September 19 | Entanglement, Bell games, randomness generation. Quantum circuit model, Solovay-Kitaev. |

September 26 | Algorithms (Grover, Simons, Hidden Subgroup, Quantum Fourier Transform) |

October 3 | Quantum Hamiltonians, Simulation, Chemistry, AdS/CFT, Blackhole Firewall Paradox |

October 10 | Quantum Machine Learning. HHL Algorithm. Phase estimation. Recommendation systems. Quantum neural networks, QRAM. |

October 17 | Quantum complexity theory. BQP and friends. QMA completeness. Lower bounds. |

October 24 | Near-term quantum computing. Quantum supremacy. BosonSampling/Random circuit sampling. Complexity theoretic evidence. |

October 31 | QAOA, variational eigensolvers, classical-quantum hybrid algorithms. Konig-Bravyi-Gosset. |

November 7 | Reading week, no class |

November 14 | Crypto I (information-theoretic). Quantum key distribution. Device-independence. Impossibility of quantum bit commitment. Coin flipping. Quantum resistant crypto. |

November 21 | Crypto II. Delegated quantum computation. Quantum money. Quantum homomorphic encryption. Entangled proof systems. |

November 28 | Grabbag. |

December 5 | Project Presentations |