An introduction to quantum error correction for mathematicians
Course notes · Eduardo Dueñez
These notes accompany a series of talks in the Quantum Error Correction Seminar at UTSA (Fall 2026). Pure states are points of complex projective spaces; quantum error correction is developed using linear lifts over $\mathbb{C}$ and binary linear algebra over $\mathbb{F}_2$, followed by a problem of classical statistical inference. Surface codes are treated in some detail, and later sections discuss belief propagation, quantum low-density parity-check codes, repeated measurements, and the statistical comparison of decoders. Undergraduate linear algebra and elementary probability are the only prerequisites.