Research

QCMA containment for Kronecker coefficient positivity (in preparation)

Goal. Understand whether hard instances of Kronecker coefficient positivity admit succinct, efficiently checkable witnesses—i.e., whether some natural formulations can be placed in a class with short classical proofs rather than fully quantum proofs.

• What I did: surveyed and reframed the problem across multiple representation-theoretic settings; built a SageMath toolkit to compute Kronecker coefficients and related data to test candidate witness families.
• Technical result: extended a known hardness result for certain 2-point correlation functions to a 3-point setting.
• Next: systematize witness families and stress-test conjectures across bases and growing n.

Learning Quantum Gibbs States Locally & Efficiently (report)

Question. When is local Hamiltonian learning from thermal (Gibbs) data identifiable, and what are the sample/time complexity tradeoffs?

• Core idea: link a Gibbs-state inner product to exponential clustering and finite-temperature Lieb–Robinson locality.
• Analysis: compare against classical Markov random field learning; reproduce variance bounds; characterize failure regimes (operator spreading / low temperature).

Quantum Optimization of MIS with Rydberg Atom Arrays (course presentation)

• Built a slide deck that synthesizes a key result on solving Max Independent Set with Rydberg-atom arrays, emphasizing the mapping from unit-disk graphs to blockade constraints.
• Explained how the paper's control knobs (Rabi frequency, detuning schedules, pulse shaping) realize analog/adiabatic and QAOA-style approaches, and where hardware constraints enter.
• Connected the method to course themes in quantum control & engineering.

Scaling PyG: Taming Massive Graphs (article + colab)

• Enabled memory-safe GNN training on commodity GPUs with neighbor/hierarchical sampling and distributed loaders in PyG.
• Assessed accuracy–time–memory trade-offs and released a minimal reproducible template with throughput metrics.