# RIT (Research Interaction Team) in Quantum Information Science, Spring 2024

### Organizers:

Yusuf Alnawakhtha, Maria Cameron, Carl Miller, Daniel Serrano, Konstantina Trivisa

### When and Where:

Mondays, 4pm, Kirwan Hall 3206

### Overview:

In this seminar, we are interested in all aspects of research at the intersection between quantum information science and mathematics. Goals for the seminar include:

- Studying recent research results in quantum information from a mathematical angle;
- Finding examples (old and new) in which existing tools from mathematics have been adapted for application in quantum information;
- Studying quantum algorithms for mathematical problems.

In the Spring 2024 semester, we will focus on hybrid talks where speakers will (i) provide an overview of their research or a QIS topic, followed by (ii) working out a mathematical concept related to the QIS topic on the board, along with the other participants. Sessions where no speakers are slotted will be used for discussion between participants about various topics, including: providing peer feedback, ethics of QIS, how to deliver effective oral presentations.

If interested in joining, reach out to Daniel Serrano (dsvolpe@umd.edu). Optional: 1 credit. Course number: AMSC689, Section 5201. Reach out to Jessica Sadler for help with registration (jsadler@umd.edu). To earn 1 credit, you need to give a talk and attend all sessions (2 excused absences allowed).

### Session 12 (04/29, 4:05pm, Kirwan Hall 3206):

**“Introduction to Quantum Error Correction Part 2: Geometrically Local Quantum Codes” - Xiaozhen Fu**

The goal of this talk is to give an overview of the advantages and disadvantages of having geometric locality in quantum error-correcting codes. Starting with an introduction to the surface code, I will highlight the nice features of a geometrically local 2D stabilizer code. However, we will also examine the limitations that arise from imposing geometric locality, and how these limitations come about, particularly with regard to the code parameters and the allowable set of logical gates. Finally, we will explore some interesting techniques such as magic state distillation and code-switching that can be used to overcome these limitations.

### Session 11 (04/22, 4:05pm, Kirwan Hall 3206):

**“Minimizing Resources for Cryptographic Proofs of Quantumness” - Carl Miller**

How can we reliably test whether a quantum computer has achieved an advantage over existing classical computers? A promising approach is to base these tests (“proofs of quantumness”) on cryptographic hardness assumptions. Such assumptions are the foundation for encryption and authentication protocols, and as such they are well-studied. Brakerski et al. (arXiv:1804.00640) introduced an interactive proof quantumness based on a standard lattice-based assumption (learning with errors). What would it take to make cryptographic proofs of quantumness realizable on near-term devices? I will explore this question and exhibit some of the mathematics involved in this topic, with a focus on the paper “Depth-efficient proofs of quantumness” by Z. Liu and A. Gheorghiu (arXiv:2107.02163).

### Session 10 (04/15, 4:05pm, PCS 1136):

**“Circuit QED Lattices: From Synthetic Quantum Systems to Spectral Graph Theory” - Alicia Kollár**

After two decades of development, superconducting circuits have emerged as a rich platform for quantum computation and simulation. When combined with superconducting qubits, lattices of coplanar waveguide (CPW) resonators can be used to realize artificial photonic materials or photon-mediated spin models. Here I will highlight the special properties of this hardware implementation that lead to these lattices naturally being described as line graphs. Elucidating this connection required combining theoretical and computational methods from both physics pure mathematics, and has lead not only to a new understanding of the physics of these devices [1,2], but also new results regarding spectral gaps of 3-regular graphs [3], and a framework for studying a new class of topologically-protected quantum error correcting codes [4].

[1] Kollár, Fitzpatrick, Houck, Nature 45, 571 (2019). [2] Kollár, Fitzpatrick, Sarnak, Houck, Comm. Math. Phys. 376, 1909-1956 (2020). [3] Kollár, Sarnak, Comm. AMS. 1, 1 (2021) [4] Chapman, Flammia, Kollár, Quantum 3, 03021 (2022)

### Session 9 (04/08, 4:05pm, Kirwan Hall 3206):

**“Group Theory and the Post-Quantum Security of SHA-3” - Joseph Carolan**

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.

### Session 8 (04/01, 4:05pm, Kirwan Hall 3206):

**“The Quantum ALU: An Exploration of Arithmetic Methods for Quantum Computers” - Addison Hanrattie**

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.

### Session 7 (03/25, 4:05pm, Kirwan Hall 3206):

**“Quantum Cryptography from Computational Assumptions” - Manasi Shingane**

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.

### Session 6 (03/11, 4:05pm, Kirwan Hall 3206):

**“Introduction to Quantum Error Correction via the 5 qubit Code” - Eric Kubischta**

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.

### Session 5 (03/04, 4pm, Kirwan Hall 3206):

**“Introduction to Unclonable Quantum Cryptography” - Yusuf Alnawakhtha**

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!

### Session 4 (02/26, 4pm, Kirwan Hall 3206):

**“Quantum Engineering 101: A Mathematical Perspective” - David Roberts**

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.

### Session 3 (02/19, 4pm, Kirwan Hall 3206):

**“On the construction of an efficient quantum algorithm: A Toolbox” - Konstantina Trivisa**

This session will discuss the construction of a quantum algorithm.

### Session 2 (02/12, 4pm, Kirwan Hall 3206):

**“The Quantum-Classical Boundary: Decoherence” - Alicia Kollár**

This session will go over basics of quantum science, which will be helpful for understanding talks on the mathematics of quantum information science the rest of this semester.

### Session 1 (02/05, 4pm, Kirwan Hall 3206):

**“Intro and Planning”**

In this session, we will provide an overview of the Spring 2024 format, obtain feedback from participants about topics of interest, and start choosing speaking slots for the rest of the semester.