Group Theory and the Post-Quantum Security of SHA-3
In this talk, I will describe a significant open problem in post-quantum cryptography: specifically the quantum security of the sponge construction with invertible permutations (which, among other things, underlies the international hash standard SHA-3). I will motivate the query model in which this problem is usually stated, and give intuition for why it is hard. Then we'll explore some recent progress on this question based on applying the theory of Young subgroups, explained in a beginner-friendly way.
The Quantum ALU: An Exploration of Arithmetic Methods for Quantum Computers
At the heart of math, physics, and computing is Arithmetic, a field that has been around throughout all of human history. However, today quantum computers provide a completely new landscape for the field. The requirements of quantum systems means that many of the standard operations one would find on a classical ALU cannot be easily implemented on quantum circuits. In this talk, I will speak on some of the new ways programmers and researchers must think when implementing arithmetic operations on quantum computers.
Introduction to Quantum Error Correction via the 5 qubit Code
In this talk, I will focus on the smallest quantum error-correcting code: the perfect 5 qubit code found by Laflamme et al. I will write down the codewords and the stabilizer generators. I will talk about which errors are correctable and how to identify and correct them via a syndrome lookup table. I will discuss the probability of getting a logical error when using a depolarizing noise channel and the resulting pseudo-threshold. Lastly I will talk about implementing logical gates via naturally fault-tolerant transversal gates.
Introduction to Unclonable Quantum Cryptography
The goal of this talk is to go over some of the intuition that lies behind quantum cryptography protocols. We will begin by addressing the advantages that quantum cryptography protocols have over classical cryptography as well as the difference between quantum and post-quantum cryptography. We will then highlight one of the advantages that quantum cryptography has, no-cloning, and discuss why it allows us to construct primitives that are impossible in the classical setting (such as position verification and unclonable encryption).
Quantum Engineering 101: A Mathematical Perspective
The theory of noise, measurement, and amplification in quantum information processing devices deviates substantially from its counterparts in conventional engineering disciplines. Quantum-mechanical systems exhibit distinctly different behavior compared to their classical counterparts, necessitating a revised theoretical framework.