Research

I work on quantum error correction: building codes and understanding how well they hold up against the noise of real devices. Recent themes are codes for bosonic modes and many-level qudits, codes built into the level structure of atoms and molecules, and small qubit codes and distillation protocols that make fault-tolerant logical gates cheaper. Each paper has a project page with a short, non-technical overview.

Bosonic QEC

2024

Quantum spherical codes

Shubham P. Jain, Joseph T. Iosue, Alexander Barg, Victor V. Albert

Nature Physics 20, 1300–1305 (2024)

Spread points out on a sphere, then superpose them: a geometric recipe for codes that protect quantum information stored in light and other oscillators.

Project page Paper arXiv

Atomic and molecular QEC

2026

Monolithic Quantum Error Correction in the Presence of Distinguishability

Shubham P. Jain, Eric R. Hudson, Wesley C. Campbell, Alexey V. Gorshkov, Victor V. Albert

arXiv preprint (2026)

Small energy shifts let the environment tell error paths apart and slowly erode codes stored inside a single atom or molecule. We quantify how fast errors must be checked to stay ahead.

Project page Paper (arXiv)
2024

Absorption-Emission Codes for Atomic and Molecular Quantum Information Platforms

Shubham P. Jain, Eric R. Hudson, Wesley C. Campbell, Victor V. Albert

Physical Review Letters 133, 260601 (2024)

Atoms and molecules mostly lose quantum information one photon at a time. Æ codes are designed around exactly that noise.

Project page Paper arXiv

Magic states

Video: Magic state factories

2026

Symmetry and AI-assisted discovery of magic-state factories

Shubham P. Jain, Adam Wills, Shraddha Singh

arXiv preprint (2026)

Group symmetry and language-model agents push the search for magic-state factories to distance three and beyond: 699 factory classes, 564 of them new, in an open database.

Project page Paper (arXiv) Factory database
2026

Classification of Generalised Triorthogonal Codes through Length 54

Adam Wills, Shubham P. Jain, Shraddha Singh

arXiv preprint (2026)

An exhaustive search of the most widely used family of magic-state distillation protocols, up to 54 input states: 74 optimal protocols, 65 of them new.

Project page Paper (arXiv)
2025

Transversal Clifford and T-gate codes of short length and high distance

Shubham P. Jain, Victor V. Albert

IEEE Journal on Selected Areas in Information Theory 6, 127–137 (2025)

The smallest known codes, up to distance 31, that apply the Clifford group or the T gate transversally, one physical qubit at a time.

Project page Paper arXiv

Qudit QEC

2026

Quantum codes in the Lee metric

Jinkang Guo, Yiqiu Han, Aranya Chakraborty, Shubham P. Jain, Tianhao Liu, Victor V. Albert, Andrew Lucas

arXiv preprint (2026)

Errors on many-level qudits are mostly small shifts, not arbitrary jumps. We build quantum coding theory around that, using the Lee metric from classical coding.

Project page Paper (arXiv)

Tutorial

2026

Quantum error correction and fault tolerance: A comprehensive tutorial

Daniel J. Spencer*, Shubham P. Jain*, Andrew Tanggara*, Zeen Sun*, Tobias Haug, Derek Khu, Kishor Bharti

arXiv preprint (2026), 209 pages

* Equal contribution

A guided introduction to quantum error correction, from repetition codes to qLDPC codes and fault tolerance. It grew out of an online lecture series in which I taught bosonic codes.

Project page Paper (arXiv)

Also on Google Scholar and ORCID.