This is an expository article aiming to introduce the reader underlying mathematics and geometry of quantum error correction. Information stored on particles subject noise interference from environment. Quantum error-correcting codes allow negation these effects in order successfully restore original information. We briefly describe necessary quantum-mechanical background be able understand how...

Because of its high data density and longevity, DNA is emerging as a promising candidate for satisfying increasing storage needs. Compared to conventional media, however, stored in subject wider range errors resulting from various processes involved the pipeline. In this article, we consider correcting duplication both exact noisy tandem duplications given length k. An inserts copy substring k ...

Random quantum dynamics generates error correcting codes that are robust against observers and errors. Here, the authors describe a simple physical picture of such codes, mapping characteristic code properties to statistical mechanics fluctuating ``entanglement domain walls''. The criterion is understood as decoupling condition walls, which leads universal scaling law ``code distance''.