I will start by introducing the concept of quantum error correction with a toy problem. Next, I will reveal the connection between the toric code and random-bond Ising model and establish its error threshold using the model's phase diagram. Finally, I will discuss efficient error correction schemes based on graph theory, Monte Carlo method, tensor networks, and machine learning approaches.

Reference: Eric Dennis, Alexei Kitaev, Andrew Landahl, John Preskill, Topological quantum memory, https://arxiv.org/abs/quant-ph/0110143