During Spring 2024, we held three reading groups in neural manifolds and TCS, quantum complexity theory, and randomness in computation.

Please see the descriptions and tables below for a summary and the list of talks for each of the groups.

This was the eighth iteration of the TCS seminar. The seminar was run by Ekene Ezeunala.

Organizer: Shujun. Graduate Student Mentor: Todd.

**Description:** This seminar aims to ground geometric conceptions of learning with learning in the brain. Manifolds are a key structure to unify these perspectives, and much of this seminar will aim to build towards understanding how they work. The first half of this seminar will build key concepts in learning over geometry, while the second half aims to use these tools to study learning in the brain.

Resource | Title | Link |
---|---|---|

Gerstner | Neuronal Dynamics | Link |

Organizers: Mark and Ryan. Graduate Student Mentor: Natalie.

**Description:** This seminar aims to explore fundamental questions about the relationship of quantum computation to classical computation through the lens of complexity theory, looking high and low for answers. We will cover quantum complexity classes such as BQP and QMA, the classical simulation of quantum circuits, Hamiltonian complexity, and classical-quantum separations for constant-depth circuits.

Resource | Title | Link |
---|---|---|

Grier | Quantum Complexity Theory | Link |

DeWolf | Quantum Computing Notes | Link |

Yuen | Advanced Topics in Quantum Information Theory | Link |

Date | Topic | Speaker | Reading |
---|---|---|---|

February 23rd | Introduction and Overview | Ryan and Mark | [O'Donnell, Wright] Lecture 01 -- Introduction to the Quantum Circuit Model. |

March 1st | Quantum complexity theory: Most functions are hard to compute, BPP ⊆ BQP ⊆ PSPACE | Shiv | DeWolf, Chapter 13 |

March 8th | Hardness of simulating depth-3 quantum circuits | Tyler | Chapter 2.5 of N. Parham (2022) |

March 15th | Break | ||

March 22nd | Efficient classical simulation of clifford circuits | Christine | Grier, Lecture 11 |

March 29th | NYC Quantum Algorithms, Complexity and Cryptography (QuACC) Day | Natalie | |

April 5th | Bravyi-Gosset-König separation between constant-depth quantum and classical circuits | Zara | DeWolf, Chapter 14 Yuen, Lecture 3 |

April 12th | QMA and the local Hamiltonian problem. | Andrew Yang, Mark | Yuen, Lecture 4 |

April 26th | The quantum PCP conjecture. | Ryan | Yuen, Lecture 5 |

Organizer: Ekene.

**Description:** In this group, we'll learn what it means to include randomness as a resource for computation. We'll look at many randomized algorithms for famous problems, look at a complexity-theoretic approach to randomness, and also discuss probabilistic proofs and methods for obtaining deterministic algorithms from existing random ones. Some background knowledge on probability is helpful but not necessary.

Resource | Title | Link |
---|---|---|

Motwani and Raghavan | Randomised Algorithms | Link |

Mitzenmacher and Upfal | Probability and Computing | Link |

Goldreich | Randomness in Computation | Link |

Date | Topic | Speaker | Reading |
---|---|---|---|

February 17th | Introduction, Las Vegas and Monte Carlo algorithms | Ekene | Chapter 1, Motwani and Raghavan; Chapters 1 and 2, Mitzenmacher and Upfal; Section 1 of Goldreich |

February 24th | Moments, Deviations, and Concentration Inequalities | Nikhil | Chapters 3 and 4 of Motwani and Raghavan, Mitzenmacher and Upfal |

March 2nd | The Probabilistic Method | Lucas | Chapter 5 of Motwani and Raghavan; Chapter 6 of Mitzenmacher and Upfal |

March 9th | Random Walks and Markov Chains | Mary | Chapter 6 of Motwani and Raghavan; Chapter 7 of Mitzenmacher and Upfal |

March 16th | Approximate Counting, Jerrum-Sinclair-Vigoda | Ekene | Chapter 11 of Motwani and Raghavan; Jerrum, Sinclair, Vigoda (2004) |

March 23rd | Pseudorandomness and Derandomisation | Ekene | Section 2 of Goldreich |

March 30th | Randomness in Sequential Computation | Lisa | Chapters 8 and 10 of Motwani and Raghavan |

April 6th | Probabilistic Proof Systems | Niko | Section 3 of Goldreich |

April 13th | Sublinear-time Algorithms with Randomness | Ekene | Section 5 of Goldreich |