Mahir Bilen Can

Professor of Mathematics

Tulane University (on leave)

Senior Quantum Architecture Scientist

Xanadu, since June 2026

I am a mathematician specializing in algebraic geometry, coding theory, and quantum error correction. Since June 2026, I have been working full-time at Xanadu Quantum Technologies as a Senior Quantum Architecture Scientist, focusing on logical prototyping and code construction. I am also a Professor of Mathematics at Tulane University, currently on leave.

My research investigates algebraic structures and their geometric manifestations: algebraic groups and monoids, representation theory, Schubert varieties, and algebraic and geometric constructions for error-correcting codes and secure communication. A growing part of this work connects mathematical structure with computational and communication problems in quantum technologies. See my CV for an overview and publications for the complete list.

I received my PhD from the University of Pennsylvania in 2006 and my BSc from METU (Turkey) in 2001. I was a Fulbright U.S. Scholar to Portugal in 2024, and I am a co-founder of the startup venture QSPARC Labs.

News

Jun 01, 2026	Joined Xanadu Quantum Technologies full-time as Senior Quantum Architecture Scientist, focusing on logical prototyping and code construction.
Jun 01, 2025	Received Tulane’s Provost’s Proof of Concept (SPARC) award for the project “Shortest Path and Antichain Metrics”.
May 01, 2024	Fulbright U.S. Scholar to Portugal, visiting Universidade Nova de Lisboa (NOVA FCT), May through August 2024.

Selected Publications

DCC
MDS Stabilizer Poset Codes

Mahir Bilen Can

Designs, Codes and Cryptography, 2026

Abs DOI Bib

Poset metrics in the context of stabilizer codes are investigated. We establish a Singleton-type bound for stabilizer poset codes and introduce the notion of MDS stabilizer poset codes. Several characterizations of these codes are obtained, including criteria in terms of additive codes and perfect codes. We also prove existence results for large families of examples, thereby extending classical results on MDS poset codes to the quantum setting.
@article{can2026mds, author = {Can, Mahir Bilen}, title = {MDS Stabilizer Poset Codes}, journal = {Designs, Codes and Cryptography}, volume = {94}, number = {8}, year = {2026}, doi = {10.1007/s10623-025-01743-4}, }

IEEE TIT

Higher Grassmann Codes III: Their Decoding and Quantum Variants

Mahir Bilen Can and R. Joshua

IEEE Transactions on Information Theory, 2025

DOI Bib

@article{can2025higher,
  author = {Can, Mahir Bilen and Joshua, R.},
  title = {Higher Grassmann Codes III: Their Decoding and Quantum Variants},
  journal = {IEEE Transactions on Information Theory},
  year = {2025},
  doi = {10.1109/TIT.2025.3596479},
}

Sigma
K-Orbit Closures and Hessenberg Varieties

Mahir Bilen Can, M. Precup, J. Shareshian, and Ö. Uğurlu

Forum of Mathematics, Sigma, 2025

Abs DOI Bib

This article explores the relationship between Hessenberg varieties associated with semisimple operators with two eigenvalues and orbit closures of a spherical subgroup of the general linear group. We establish the specific conditions under which these semisimple Hessenberg varieties are irreducible. We determine the dimension of each irreducible Hessenberg variety under consideration and show that the number of such varieties is a Catalan number. We then apply a theorem of Brion to compute a polynomial representative for the cohomology class of each such variety. Additionally, we calculate the intersections of a standard (Schubert) hyperplane section of the flag variety with each of our Hessenberg varieties and prove that this intersection possesses a cohomological multiplicity-free property.
@article{can2025korbit, author = {Can, Mahir Bilen and Precup, M. and Shareshian, J. and U{\u g}urlu, {\"O}.}, title = {K-Orbit Closures and Hessenberg Varieties}, journal = {Forum of Mathematics, Sigma}, volume = {13}, pages = {e103}, year = {2025}, doi = {10.1017/fms.2025.10063}, }

Irreducible Unipotent Numerical Monoids

Mahir Bilen Can and N. Sakran

Semigroup Forum, 2024

DOI Bib

@article{can2024irreducible,
  author = {Can, Mahir Bilen and Sakran, N.},
  title = {Irreducible Unipotent Numerical Monoids},
  journal = {Semigroup Forum},
  volume = {109},
  number = {2},
  pages = {243-278},
  year = {2024},
  doi = {10.1007/s00233-024-10442-5},
}

DCC

Defects of Codes from Higher Dimensional Algebraic Varieties

Mahir Bilen Can, R. Joshua, and G. V. Ravindra

Designs, Codes and Cryptography, 2024

DOI Bib

@article{can2024defects,
  author = {Can, Mahir Bilen and Joshua, R. and Ravindra, G. V.},
  title = {Defects of Codes from Higher Dimensional Algebraic Varieties},
  journal = {Designs, Codes and Cryptography},
  volume = {92},
  number = {2},
  pages = {477-494},
  year = {2024},
  doi = {10.1007/s10623-023-01317-2},
}