Collin Yuanjie Ren

PhD in Physics, MIT · September 2026

I completed my PhD in Physics at MIT in September 2026, under the supervision of Peter Shor and Aram Harrow. Previously, I earned my MA in Physics at Stony Brook University, where I was advised by Axel Drees.

My research focuses on quantum codes, topological order, and quantum simulation of physical systems. I'm also learning about open quantum systems, quantum complexity theory, as well as quantum algorithms.

In my free time, I think about and experiment with how machine learning can help derive and prove mathematical theorems (auto-formalization) and how large language models can facilitate the design of better video games.

Photo of Collin Yuanjie Ren
yuanjie[at]mit[dot]edu
MIT Physics Department
Cambridge, MA

Research

My research spans three complementary areas at the intersection of quantum information and theoretical physics:

01

Topological Quantum Codes

Developing quantum error-correcting codes and understanding their connections to topological phases of matter, including universal circuit constructions and phase transitions.

Topological Order Circuit Design Phase Transitions
02

Agent for Math & Physics

Building MerLean, an AI system for Lean-based autoformalization, formal verification, and automated theorem proving, from quantum computation papers to graduate-school-level math benchmarks.

Auto-formalization Lean 4 / Mathlib LLM Agents
03

Quantum Simulation

Simulating physical systems on quantum computers, including fermionic tensor networks and adaptive quantum circuits.

Tensor Networks Adaptive Circuits

Startup Exploration

We are considering a startup around formal verification and automated mathematical theorem proving, and we are actively looking to speak with people interested in investing in this direction.

Publications

Convex-Gaussianity of fermionic Gibbs states in perturbation theory
Kaifeng Bu, Yuanjie Ren
arXiv:2609.09608, preprint (2026)
arXiv
Fermionic Systems Statistical Mechanics Quantum Simulation
Maximizing Algebraic Connectivity with 2(n-2) Edges: The Large Vertex Number Case
Zeru Zhu, Jinzheng Li, Yuanjie Ren, Ji Liu
arXiv:2608.07360, preprint (2026)
arXiv
Graph Theory Spectral Theory Formal Verification
MerLean-Prover: A Recursive Looping Harness for Lean 4 Theorem Proving
Jinzheng Li*, Zeru Zhu*, Yuanjie Ren* (equal contribution)
arXiv:2605.26959, preprint (2026)
arXiv
Theorem Proving Lean 4 AI Agent
Thermodynamic Irreversibility of Training Algorithms
Liu Ziyin*, Yuanjie Ren*, Adam Levine, Isaac Chuang (equal contribution)
arXiv:2605.21933, preprint (2026)
arXiv
Statistical Mechanics Artificial Intelligence Machine Learning
MerLean: An Agentic Framework for Autoformalization in Quantum Computation
Yuanjie Ren*, Jinzheng Li*, Yidi Qi* (equal contribution)
2026
arXiv
Auto-formalization AI Agent Machine Learning Quantum Computation
Graphical Calculus For Fermionic Tensor Networks
Yuanjie Ren, Kaifeng Bu, Andreas Bauer
arXiv Talk
Quantum Simulation Tensor Network Fermionic Systems
A Universal Circuit Set using the S3 quantum double
Liyuan Chen, Yuanjie Ren, Ruihua Fan, Arthur Jaffe
npj Quantum Inf. 11, 112 (2025)
Paper
Quantum Error Correction Quantum Computation Topological Order Circuit Design
Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits
Yuanjie Ren, Nathanan Tantivasadakarn, Dominic J. Williamson
Phys. Rev. X 15, 031060 (2025)
Paper Talk
Topological Order Adaptive Circuits Quantum Computation Quantum Simulation
Topological quantum computation assisted by phase transitions
Yuanjie Ren, Peter Shor
arXiv Talk
Topological Order Quantum Computation Phase Transitions Modular Tensor Categories
Examination of the universal behavior of the η-to-π0 ratio in heavy-ion collisions
Yuanjie Ren, Axel Drees
Phys. Rev. C 104 054902 (2021)
Paper
Machine Learning Quark-Gluon Plasma Nuclear Physics

Education

Doctor of Philosophy (Quantum Computation) GPA: 5.0/5.0
Massachusetts Institute of Technology (September 2020 – September 2026)
Main Courses: Quantum Information Science II & III, Quantum Field Theory II & III, General Relativity, Algebraic Topology, Manifold Analysis, Holography, String Theory
Master of Arts (Nuclear Physics) GPA: 3.95/4.00
Stony Brook University (2018 – 2020)
Main Courses: String Theory I & II, Mathematical Physics, Nuclear Physics, Quantum Field Theory I, Group Theory

AI Agent for Math & Physics

I'm building MerLean, a research system for Lean-based autoformalization, formal verification, and automated theorem proving, together with Jinzheng Li from NEU and Yidi Qi from NEU, and Zeru Zhu.