Fernando Granha Jeronimo

About me

My research is in theoretical computer science (TCS), mainly involving:

• Coding Theory
• Expanders and High-dimensional Expanders
• Optimization, such as the Sum-of-Squares hierarchy
• Quantum Computing

Interactions among these areas are very present in my research. In particular, I love expansion (broadly defined) since it provides an amazing lens to explore and understand phenomena in all the above areas. I am also particularly intrigued by the many connections between CS theory and mathematics. Glimpses on some of my interests in coding theory and expanders can be found in short talks at IAS here and here.

I am looking to continuously grow my research group over the years. Motivated students are encouraged to apply to our graduate programs.

Teaching

CS 498: Introduction to Quantum Computing (Spring 2026) Interactive companion Quantum Interactive Course

CS 579: Computational Complexity (Fall 2025)

CS 498: Introduction to Quantum Computing (Spring 2025)

CS 598: Expansion, Codes, and Optimization both Classical and Quantum (Fall 2024)

PhD Students

• Asymptotically Good Quantum Locally Testable Codes
  (with William Gay)
• Subspace-Design Codes from LCL Derandomization: A Short Note
  (with Nikhil Shagrithaya)
• Stable Regularity Lemmas: Efficient Algorithms and Essentially Tight Littlestone Bounds
  (with Leonardo Nagami Coregliano)
• Algorithmic List Decoding at Capacity and Optimal Proximity Gaps for Reed–Solomon Codes
  (Fernando Granha Jeronimo)
• Explicit Capacity-Achieving Quantum LDPC Codes List Decodable in Near-linear Time
  (with William Gay and Abhi Shukul) SODA 2027 (to appear)
• Quantum List Recovery and Decoding: Achievability and Limitations
  (with Xiaojuan Ma)
• From Random Quantum Codes to Explicit qLDPC Codes via Local Properties
  (with Xiaojuan Ma and Nikhil Shagrithaya)
• The Honeycomb Framework for Code Bounds
  (with William Gay and Lenny Liu)
• Dimension-Free Polylogarithmic Quantum Shadow Tomography from Sequential PGM
  (with Qizhao Huang and Lenny Liu)
• PureSuperQMA(exp) = BellPureSymQMA(poly) = QMA via Dimension-Free Bosonic Argmax
  (with William Gay, Lenny Liu, Itai Leigh, Pei Wu and Haochen Xu)
• Optimal Quantum de Finetti Theorems via Argmax Rounding
  (with Pei Wu and Haochen Xu)
• An Argmax Principle for Sum-of-Squares Relaxations on the Sphere
  (with Pei Wu and Haochen Xu)
• The Collapse of Unentangled Stoquastic Merlin-Arthur Proof Systems
  (with William Gay)
• An Optimal Analysis of the Product Test
  (with Jacob Beckey and Pei Wu)
• Probabilistic Guarantees to Explicit Constructions: Local Properties of Linear Codes
  (with Nikhil Shagrithaya) STOC 2026
• A Framework for CSPs over the Hypercube: from Sublinear to Subexponential Time
  (with Agastya Vibhuti Jha and Davide Mazzali)
• List Decoding Expander-Based Codes via Fast Approximation of Expanding CSPs: I
  (with Aman Singh)
• Higher-order Delsarte Dual LPs: Lifting, Constructions and Completeness
  (with Leonardo Nagami Coregliano, Chris Jones, Nati Linial and Elyassaf Loyfer) ITCS 2026
• Pseudorandomness of Expander Walks via Fourier Analysis on Groups
  (with Tushant Mittal and Sourya Roy) RANDOM 2025
• Explicit Codes approaching Generalized Singleton Bound using Expanders
  (with Tushant Mittal, Shashank Srivastava and Madhur Tulsiani) STOC 2025(invited to special issue)
  slides @CS Seminar
• List Decoding Explicit Binary Codes Near Capacity at (semi-)Structured Centroids
  (Fernando Granha Jeronimo)
• Coherence in Property Testing: Quantum-Classical Collapses and Separations
  (with Nir Magrafta, Joseph Slote and Pei Wu) QIP 2025
  video @QIP'25
• List Decodable Quantum LDPC Codes
  (with T. Bergamaschi, T. Mittal, S. Srivastava and M. Tulsiani) QIP 2025 (poster)
• Pseudorandom and Pseudoentangled States from Subset States
  (with Nir Magrafta and Pei Wu) TQC 2024 (poster)
• Dimension Independent Disentanglers from Unentanglement and Applications
  (with Pei Wu) CCC 2024
• List Decoding of Tanner and Expander Amplified Codes from Distance Certificates
  (with Shashank Srivastava and Madhur Tulsiani) FOCS 2023
• The Power of Unentangled Quantum Proofs with Non-negative Amplitudes
  (with Pei Wu) STOC 2023 (QIP 2024)
  video @STOC'23
• Fast Decoding of Explicit almost Optimal \(\epsilon\)-balanced \(q\)-ary Codes and
  Fast Approximation of Expanding \(k\)-CSPs
  (Fernando Granha Jeronimo)RANDOM 2023
• Exact Completeness of LP Hierarchies for Linear Codes
  (with Leonardo Nagami Coregliano and Chris Jones) ITCS 2023
  video @ITCS
• Almost Ramanujan Expanders from Arbitrary Expanders via Operator Amplification
  (with Tushant Mittal, Sourya Roy and Avi Wigderson) FOCS 2022(invited to special issue)
  video @IAS video @Princeton
• A Complete Linear Programming Hierarchy for Linear Codes
  (with Leonardo Nagami Coregliano and Chris Jones) ITCS 2022
  video @IAS
• Explicit Abelian Lifts and Quantum LDPC Codes
  (with Tushant Mittal, Ryan O’Donnell, Pedro Paredes and Madhur Tulsiani) ITCS 2022
  video @IAS
• Near-linear Time Decoding of Ta-Shma's Codes via Splittable Regularity
  (with Shashank Srivastava and Madhur Tulsiani) STOC 2021
  video @STOC'21 slides @STOC'21 video @JTW'20 slides @Junior Theorists Workshop'20
• Unique Decoding of Explicit \(\epsilon\)-balanced Codes Near the Gilbert-Varshamov Bound
  (with Dylan Quintana, Shashank Srivastava and Madhur Tulsiani) FOCS 2020(invited to special issue)
  longer video @FOCS20 longer slides @FOCS20 slides general CS audience
• Sum-of-Squares Lower Bounds for Sherrington-Kirkpatrick via Planted Affine Planes
  (with Mrinalkanti Ghosh, Chris Jones, Aaron Potechin and Goutham Rajendran) FOCS 2020
• Tighter Bounds on the Independence Number of the Birkhoff Graph
  (with Leonardo Nagami Coregliano) European J. of Combinatorics
• List Decoding of Direct Sum Codes
  (with Vedat Levi Alev, Dylan Quintana, Shashank Srivastava and Madhur Tulsiani) SODA 2020
  slides @SODA20
• Approximating Constraint Satisfaction Problems on High-Dimensional Expanders
  (with Vedat Levi Alev and Madhur Tulsiani) FOCS 2019

Other Writings

A Constrained Random Walk Through Coding Theory
(Fernando Granha Jeronimo) Dissertation

Short Bio

Prior to UIUC, I was a Simons-Berkeley fellow, and thankfully supported in part as a Google Research Fellow. I had a wonderful experience as a postdoc in Avi Wigderson's group at the Institute for Advanced Study (IAS). I obtained my PhD from UChicago. I received a B.Sc. and M.Sc. degrees from Unicamp Brazil (my home country) and also received an engineering degree from Telecom Paris (France) as part of a double degree program.

Research Courses

Code Bounds: A (Crude) Course

Reading Groups in Theory

Reading Group on TCS - Spring 2026

Reading Group on TCS - Fall 2025

Around Classical and Quantum PCPs

Previous Reading Group on Expansion and Coding Theory (IAS+Princeton University)

Previous External Speaker Series.

Previous Reading Group on Coding Theory

Previous Reading Group on High-dimensional Expanders

Local-to-Global Mentorship Program

Local-to-Global TCS Mentorship Program at UIUC

Past Teaching Activities

I was a TA 14 times for various courses during my PhD receiving two (annual) TA prizes from the CS department.