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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
Pages
Posts
Will Mathematics Become Art?
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Matchgates, Majoranas, and Lie Algebras: A Self-Contained Guide
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Today I set out to understand a deceptively simple question: why does a circuit family built from \(Z\)-rotations and nearest-neighbor \(XX\)-rotations lead so naturally to Lie algebras, Majorana operators, and the rotation group \(SO(2n)\)?
A Place for Questions in Progress
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Research rarely begins as a finished paper. More often, it starts with a question, a partial connection, or the feeling that an idea from one field might help clarify a problem in another.
portfolio
talks
Classification of Large-Scale Lyme Disease Data Permalink
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Presented the methods and findings of the associated technical report on classification and analysis of large-scale Lyme disease data.
Image Segmentation with Kernel Flow Algorithm Permalink
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Presented work with Houman Owhadi and Lei Zhang on image segmentation using the Kernel Flow algorithm.
METTS Sampling and Free Energy Computation
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Seminar on METTS (Minimally Entangled Typical Thermal State) sampling algorithms and their application to computing free energies in quantum many-body systems.
Quantum numerical linear algebra junior participant introduction talk
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Introductory talk as junior participant in IPAM program on quantum numerical linear algebra, discussing connections between classical and quantum approaches to linear algebra problems.
Approximation of Free Energies with Fluctuation Relations on Quantum Hardware Permalink
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Presented quantum algorithms and computational results for approximating free energies using fluctuation relations on quantum hardware. The meeting record is Bulletin of the American Physical Society 67(3), Abstract B01.00008.
Quantum computing for scientific computation
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Virtual seminar presentation at Shanghai Jiao Tong University on quantum materials and quantum information science research.
Quantum dynamics for incommensurate system
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Presented research on understanding quantum dynamics in incommensurate systems, with applications to moiré materials and twisted bilayer graphene structures.
Quantum algorithms and applications in materials science
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Presented as young researcher in the IPAM Quantum Long Program, discussing recent advances in quantum algorithms and their applications to materials science problems.
Introduction to Block Encoding
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Introductory seminar on block encoding techniques in quantum computation, covering fundamental concepts and applications to quantum simulation and quantum linear systems problems.
Improving DFT simulation for Twisted Bilayer Graphene
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Discussed improvements to density functional theory (DFT) simulations for twisted bilayer graphene, addressing computational efficiency and accuracy in modeling moiré superlattice structures.
Data Driven Approach for Local Density of State on the Moiré Scale
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Presented data-driven machine learning approach to understanding and predicting local density of states in moiré materials, combining physics-informed methods with deep learning for efficient materials discovery.
From Hype to Prototype, a mathematical introduction to quantum computing and quantum error correction
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I will give a basic introduction of quantum computing and try to touch base on the quantum algorithms and quantum error correction.
Introduction to block encoding
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With recent advancements in quantum hardware and the implementation of quantum error correction codes, the prospect of developing an early fault-tolerant quantum computer within the next two decades has become increasingly promising. The potential applications of such a quantum computer, particularly in solving complex problems in quantum chemistry or quantum many-body systems, are garnering significant attention. In this talk, we aim to provide an in-depth introduction to Block Encoding, a pivotal first step in unlocking the capabilities of quantum computers for these applications. Our discussion will delve into the latest developments of block encoding, explore a fundamental theorem related to this technique.
Scientific computing with quantum and AI: New frontiers
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In recent years, scientific computing has been transformed by rapid advancements in quantum computing and artificial intelligence (AI). This talk will explore how these technologies are reshaping complex computational landscapes, from operator learning in condensed matter physics to simulation of quantum dynamics.
Early Fault-Tolerant Block Encoding with Low Clifford+T Count for Second Quantized Hamiltonian Permalink
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Presented fault-tolerant block-encoding constructions with reduced Clifford+T costs for second-quantized Hamiltonians.
Early Fault-Tolerant Block Encoding with Low Clifford+T Count for Second Quantized Hamiltonian Permalink
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Joint presentation with Shuchen Zhu on low-overhead block encoding for early fault-tolerant quantum simulation.
Block encoding with low gate count for second quantized Hamiltonian
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Presented work on efficient block encoding techniques for quantum simulation with reduced gate count requirements, focusing on second-quantized Hamiltonians for quantum chemistry and materials science applications.
High-Order Magnus Expansion for Hamiltonian Simulation Permalink
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Research update on high-order Magnus expansions for time-dependent Hamiltonian simulation.
A Framework for Driven Dissipative Ground State Preparation Permalink
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Lightning presentation and poster on open-system methods for quantum ground-state preparation.
Fusion of Multi-Scale Analysis and Open Systems: A Future of Quantum Materials Science Permalink
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Tutorial connecting multiscale analysis, open quantum systems, and mathematical modeling for quantum materials.
Magic State Distillation Using Asymptotically Good Codes on Qudits Permalink
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Presented joint work on magic-state distillation using asymptotically good codes on qudits.
Beyond Lindblad Dynamics: Rigorous Guarantees for Thermal State Permalink
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Seminar presentation on rigorous guarantees for thermal-state preparation beyond Lindblad dynamics.
Quantum State Preparation with Sampling Permalink
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Research update on sampling-based methods and resource considerations for quantum state preparation.
Driven Dissipative Ground State Preparation Permalink
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Invited presentation on driven dissipative approaches to quantum ground-state preparation.
Fault-Tolerant Block Encoding for Second-Quantized Hamiltonians Permalink
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Minisymposium presentation on fault-tolerant block-encoding constructions for second-quantized Hamiltonians.
Data-driven approach for searching flat band and low energy approximation for TMD
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Invited talk at Yuan Cao’s Quantum Materials Seminar on data-driven approaches to searching for flat bands and low-energy approximation for TMD.
Continuum limit for one-dimensional TMD-like heterostructures
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Contributed talk at the 2026 SIAM Northern and Central California Section Conference on the continuum limit for one-dimensional TMD-like heterostructures. The conference takes place October 26–27, 2026; the individual talk date is to be confirmed.
teaching
Calculus I
Teaching Assistant, University of Minnesota, 2019
Teaching assistant for MATH 1271 Calculus I, supporting lectures, grading, and recitations.
Multivariable Calculus
Teaching Assistant, University of Minnesota, 2020
Teaching assistant for MATH 2263 Multivariable Calculus, with responsibilities including grading and student support.
Calculus I
Instructor, University of Minnesota, 2022
Instructor for MATH 1271 Calculus I.
CSE Multivariable Calculus and Vector Analysis
Computer Lab Instructor, University of Minnesota, 2024
Led computer lab instruction for MATH 2374 CSE Multivariable Calculus and Vector Analysis.
Mathematics of Quantum Computing
Grader, University of Minnesota, 2024
Grader for MATH 5590 Mathematics of Quantum Computing.