Since 2023, I have had the privilege of being part of the Semeghini lab, which aims to build a dual-species Rubidium-Ytterbium neutral atom array with continuous reloading. This experience has been instrumental in shaping my understanding of the connection between physics and computation; it helped me gain…
FreeAlgebra supports the differentiable manipulation of freely-generated algebras. It is an offshoot project of the theoretical research on fermionic Gaussian computation and a nice implementation practice for the theory of finitely-generated algebras.
The motivation for this final project is the adjoint problem of Hamiltonian mechanics: understanding how the evolution of a subsystem can be used to infer properties of the composite system. The goal is characterizing dynamical closures—the extension of subsystem dynamics into the Hamiltonian dynamics of a larger system. This problem is not solved by this project. However, the steps towards solving this problem provided insights into the relation between kinematics and dynamics, as well as the boundary between classical and quantum theories.
This final project explores the hypergraph product of convolutional codes. It is part of a research project conducted at MIT’s Shor group in collaboration with Zhiyang He, Andrey Boris Khesin, Jonathan Lu, and Peter Shor. The focus is on exploring quantum CSS codes through the lens of hypergraph products and convolutional code techniques.
Published on arXiv, 2024
This work defines fermionic quantum convolution and demonstrates the unique entropy-invariance of fermionic Gaussian states under convolution. It demonstrates that many desirable classical statistical and information-theoretic properties of Gaussian states and convolution have counterparts in the fermionic quantum algebra. Click on the section title to see details.
Published on Journal of Physics A: Mathematical and Theoretical, 2025
This work extends fermionic Gaussian theory by studying the displaced (nonzero mean) case, resulting in extended matchgate classical simulation, wider applicability of fermionic convolution, and a more generalized understanding of fermionic Gaussian computation beyond the constraint of parity super-selection. Click on the section title to see details.
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Course notes for Harvard CS 121: Theoretical Computer Science (Fall 2022, Boaz Barak). Provides foundational knowledge in computability and complexity, as well as strong intuitions on computational models and fundamental limits of computation; my favorite computer science course at Harvard.
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Course notes for MIT 8.3710(Fall 2022, Peter Shor), a introductory graduate course in quantum computation. Features the basics of quantum circuits, Grover and Shor’s algorithms, quantum channels and error-correction.
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Self-study notes for tensor and exterior algebra, differential forms, quaternions, and basic differential geometry.
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Self-study notes for Tom Leinster’s Basic Category Theory Chapters 1-4, covering basic definitions, adjunction, representables, and universal constructions.
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Self-study notes on MacLane and Birkhoff’s Algebra. These notes cover topics roughly equivalent to a one-semester undergraduate course on group and ring theory.
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Course notes for Physics 143b: Quantum Mechanics II (Fall 2023, Sonia Paban) at Harvard. Many constructions were later much better understood after taking classical mechanics.
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Course notes for Stat 111: Statistical Inference (Spring 2024); the bread and butter of classical inference.
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Research notes including hyperbolic groups, Dehn algorithm, and Svarc-Milnor lemma. Part of an incomplete research project (suspended).
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Course notes of Harvard Math 114 (Fall 2024). It reinforces the mathematical foundations for a rigorous understanding of information theory and infinite-dimensional physical systems.
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Teaching assistant material of Harvard Physics 151: Mechanics (Fall 2024, Arthur Jaffe). It provides a mathematical perspective on the boundary between classical and quantum mechanics, with applications ranging from symmetry principles to field theory.
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Comprehensive course notes for MIT 6.370 Information Theory: from Coding to Learning, (Fall 2024, Yury Polyanskiy) This is a very fast-paced, graduate-level treatment of modern information theory.
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Self-learning notes for reinforcement learning at introductory graduate level. Covers classical MDP theory as well as modern toolkits applicable to relaxed assumptions and learning-based methods.
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Continuously updated self-learning notes for cool machine learning theory and papers. Includes diffusion and flow matching, NeurODE, and more.