Introduction to Quantum Error Correction (QEC)

Abstract

Quantum error correction addresses a problem with no classical counterpart: protecting an unknown quantum state from noise, when measuring the state disturbs it and the possible errors form a continuum. The resolution, found in the mid-1990s, is algebraic. Suitably chosen commuting measurements produce a binary syndrome that identifies the error without revealing the encoded state, and correcting finitely many errors turns out to correct all of their linear combinations. This talk introduces these ideas from a mathematical point of view, organized around stabilizer codes. It is the first of a short series leading to surface codes and to decoding, which is at heart a problem of statistical inference. Only undergraduate linear algebra and elementary probability are assumed; no background in quantum mechanics is required.

Notes for the series are linked above; the explicit calculations for this session are collected in a two-page sheet.