Nicholas Connolly
Email: nicholas.connolly@oist.jp
I am currently working at the Okinawa Institute of Science and Technology (OIST) in Okinawa, Japan as a postdoc in the Quantum Information Science and Technology Unit (Nemoto Unit).
From 2021 through August, 2023 I worked as a postdoc at Inria, the National Institute for Research in Digital Science and Technology, in Paris, France. My project was related to quantum error correction.
I received a PhD in mathematics from the University of Iowa in 2021. My research focused on knot theory and the tabulation of 2-string tangles.
Graduate Research
My graduate research focused on the knot theoretic structures known as tangles. A tangle can be understood as a sphere embedded with multiple entwined strings. While a tangle is a three dimensional object, mathematicians study them using tangle diagrams, the projected shadow of a tangle onto a two dimensional surface. The primary way to study tangles is through exploring the combinatorics of tangle diagrams.
The goal of my research is to exhaustively tabulate and classify 2-string tangles up to a fixed crossing number. I am creating a database to enumerate the preferred constructions for known tangles together with their structural properties. Tangles can be divided into families based on their construction. Some families are well understood while others have not yet been classified uniquely. In addition to computationally constructing a database, I am also working to improve the theoretical description of these tangle families. In particular, I am using graph theory to classify non-algebraic tangle diagrams.
Links
Research Statement (2021)
Recent Presentations
December 2025 invited presentation at the Quantum Error Correction Theory Workshop for Young Researchers at Nagoya University: A Brief Overview of some Quantum Erasure Decoding Algorithms
July 2025 poster presentation at Quantum Innovation 2025 in Osaka: Exploring Graph State Local Equivalence Classes with Distance Hereditary Split Decompositions
August 2024 poster presentation at the Asian Quantum Information Science Conference in Sapporo: An Efficient Erasure Decoder and Quantum Multiplexing Using Hypergraph Product Codes
March 2023/2024 invited presentations at the 2023/2024 YITP Quantum Error Correction Workshops at the University of Kyoto: VH Decoder for HGP Codes in the Erasure Channel (2024); Fast Erasure Decoder for a Class of Quantum LDPC Codes (2023) (https://arxiv.org/abs/2208.01002)
February 2023 poster presentation at QIP2023: Fast Erasure Decoder for a Class of Quantum LDPC Codes (https://arxiv.org/abs/2208.01002)
November 2022 invited tutorial at the Quantum Information Center Sorbonne workshop: An Introduction to Quantum Error Correction
February 2022 Kenyon College Math Monday Presentation: An Introduction to Rational Tangles and Some of Their Generalizations
Fall 2020 SCMB Poster Presentation: A Database of Tangles: Knot Theoretic Models for DNA Topology
Summer 2020 presentation on NSF MSGI research internship: Multi-Modal Community Detection with Multi-Weighted Graphs
Fall 2019 presentation on generalized planar diagram notations for tangles: Constellations and an Algebraic Planar Diagram Code
ACML 2019 poster presentation on summer research in machine learning: Using Artifical Intelligence to Automate Body Movement Analysis (short paper)
Fall 2019 presentation on searching for internship opportunities as a graduate student in mathematics: Exploring Industry as a Pure Mathematcian
Spring 2019 research on using graph theory to describe tangle diagrams: Describing Non-Algebraic Tangles with Graphs
Fall 2018 research in the computational construction of 2-string tangles: Tabulation and Classification of 2-String Tangles
Summer 2014 research in coding theory: Constructing Linear Codes with Record Breaking Parameters
Math and Science Outreach events in Japan
These events are designed to introduce middle school and high school students to the world of science and mathematics, and involve making presentations and leading group activities.
October 2025, Science Day Gunma 2025--The World of Quantum Mechanics, science outreach presentation at Gunma University: Graph Local Equivalence Classes
August 2024 and 2025, Onna x OIST Children's School of Science 2025, science outreach presentation at OIST: Mathematics with Games
2025, Science outreach presentations for middle school students visiting OIST: Thinking Mathematically: Searching for Patterns! (Japanese language version)