Abstract: Mathematical innovation has been crucial in quantum information science since its inception, and the relationship between the two fields is vital and evolving. While the theory of quantum information depends most directly on linear algebra and probability, other mathematical connections appear in quantum research that are diverse and often surprising. This talk will offer a personal perspective on the interaction between quantum and math. We will discuss an example from the field of quantum cryptography. The talk serves as a kickoff to a series of seminars under UMD's new MathQuantum RTG program ( https://mathquantum.umd.edu ).
Abstract: First session of the Quantum Information RIT. We will give an overview of the format for this semester, and plan logistics for the rest of the term. This will include the option for participants to start signing up for presentation slots.
Abstract: This talk will introduce fundamentals of quantum science that will be useful for better understanding mathematics of quantum information science
Abstract: 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. In this talk, I will provide a mathematical viewpoint on the theory of quantum noise. As an illustrative example, I will study a quantum-information-theorist's version of a classical Markov chain and demonstrate how the theory deviates from classical expectations.
Abstract: 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). A main goal of the talk is to demystify some of the vocabulary and concepts often used in this field, so questions are very much encouraged!
Abstract: Cryptographic protocols with computational security are those that obtain security by restricting adversaries to only perform efficient actions. In the quantum setting, computational assumptions have been used to construct secure quantum protocols that utilize only classical communication. In this talk, I will focus on a primitive known as Trapdoor Claw-Free (TCF) Functions. TCFs have been used to construct many quantum protocols that only utilize classical communication. I will discuss their construction and explain how their properties can be used to obtain security against quantum adversaries.
Abstract: 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. I will also explore how new ideas from Quantum Information Science like the QFT have led to new ways of doing arithmetic.
Abstract: 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.
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