Sujeet Bhalerao

I am a PhD student in mathematics at the University of Illinois Urbana-Champaign, advised by Felix Leditzky. I work on quantum communication and channel capacities using tools from optimization and representation theory.

Previously I completed my BS-MS in mathematics at the Indian Institute of Science Education and Research (IISER) Pune. I wrote my master's thesis on "Stiefel-Whitney classes of representations of dihedral and symmetric groups", focusing on questions at the intersection of group cohomology and representation theory.

Email  /  GitHub  /  LinkedIn

Research

• Improving quantum communication rates with permutation-invariant codes
  Sujeet Bhalerao, Felix Leditzky
  arXiv preprint, 2025. Accepted at QIP 2026. [arXiv] [Code]
• Stiefel-Whitney classes of representations of dihedral groups
  Sujeet Bhalerao, Rohit Joshi, Neha Malik
  Communications in Algebra, 2025. [Journal] [arXiv]
• Stiefel-Whitney classes of representations of dihedral and symmetric groups
  Master's thesis at IISER Pune, supervised by Steven Spallone. Thesis: [Link]

Workshop paper

• Evolving graph codes with improved error thresholds for Pauli channels
  Sujeet Bhalerao
  Machine Learning and the Physical Sciences (ML4PS) Workshop, NeurIPS 2025. [Paper]

Notes

• Fall 2022, Math 595: Representation Theoretic Methods in Quantum Information [PDF].

Code

• compact-letter-display - Python package for compact letter displays from ANOVA post-hoc tests. [PyPI] [GitHub]
• Quantum Channel Zoo - Database of quantum channels and their mathematical and information-theoretic properties. Built as a project for the Illinois Mathematics Lab. [GitHub]
• \(2\)-Sylow Restriction Decomposition - SageMath scripts for decompositions of irreducible representations of the symmetric group when restricted to a \(2\)-Sylow subgroup.
• Clustering Math Departments - Tools for clustering math department faculty into research areas using publication data. [MathSciNet scraper] [arXiv API] [Community detection]

Teaching

Illinois Mathematics Lab

The Illinois Mathematics Lab provides a framework for faculty and graduate students to engage local undergraduates in research. I have been a graduate student mentor for the following projects as part of the Illinois Mathematics Lab. Click a project to expand details.

• Fall 2023: The Quantum Channel Zoo

  The goal of this project is to map out the “quantum channel zoo” by creating a website hosting a database of the known quantum channels and their mathematical and information-theoretic properties.

  Project site: quantumchannelzoo.org

• Spring 2023: Uniform Distribution and Rigidity

  This project was an exploration of many interesting facts and conjectures related to uniform distribution and rigidity. There were numerous sub-projects, which included: looking for computational evidence for uniform distribution of fractional parts of powers of rationals, testing the efficacy of low discrepancy sequences for numerical integration, and numerically estimating the ratio of the smallest gap to the largest gap in the three-gap theorem.

  There was also a theoretical component, which included understanding the connection between Farey sequence and diophantine approximation, and surveying statements involving the Farey series that are equivalent to the Riemann hypothesis.

• Fall 2022: Quantum Teleportation and Quantum State Discrimination

  Quantum teleportation is a fundamental task in quantum information theory wherein two parties Alice and Bob use a shared entangled quantum state and classical communication to teleport an unknown quantum state.

  This task is mathematically equivalent to a certain quantum state discrimination problem, where the goal is to perform a measurement that optimally distinguishes among a given set of quantum states.

  This problem in turn has a useful description in terms of a class of optimization problems called semidefinite programs (SDP).

  These SDPs are a generalization of linear programs with a nice duality theory and efficient solvers available in Python and MATLAB. In particular, we numerically determine the optimal measurement, as measured by fidelity, for various quantum states with a given form. We show that adding noise to the state can in fact increase fidelity, confirming and extending previous results. Furthermore, we characterize the set of states that attain the highest fidelity and plot related values.

• Spring 2022: Studying the Math Department’s Structure

  What is our department good at? The question is not as simple as it seems: the research group composition changes fast, and their impact on the global scale might be smaller or larger than it seems.

  The goal of this project is two-fold: on one hand, to detect the intrinsic research clusters (i.e., groups of people working in close areas, talking to the same communities, publishing in the same journals) within the department. On the other hand, to see how significant these clusters are in the context of their respective fields: which are strong, which are growing...

Teaching assistant

• Fall 2020: Math 220 (Calculus)
• Spring 2021: Math 234 (Business Calculus)
• Fall 2021: Math 221 (Calculus I)
• Spring 2022: Math 257 (Linear Algebra with Computational Applications)
• Summer 2022: NetMath 415 (Linear Algebra)

Grader

• Spring 2021: MATH 444 (Elementary Real Analysis)
• Fall 2022: MATH 564 (Applied Stochastic Processes)
• Fall 2022: MATH 285 (Differential Equations)
• Fall 2022: MATH 442 (Intro Partial Differential Equations)
• Spring 2023: MATH 415 (Applied Linear Algebra)
• Spring 2023: MATH 540 (Real Analysis)
• Spring 2023: MATH 466/564 (Applied Stochastic Processes)

Template adapted from Jon Barron's website.