Quantum Codes as Robust Phases of Matter

Explore a lecture by Andrew Lucas that delves into the profound connection between quantum error correction and phases of matter for spatially local codes in finite dimensions. Learn how this analogy extends to more general settings, particularly how quantum codes with check soundness function as absolutely stable phases of matter. Discover insights about constant-rate quantum low-density parity-check codes and their implications for the third law of thermodynamics, demonstrating the existence of absolutely stable phases of matter with constant entropy density at zero temperature. The presentation also covers the robustness of the toric code phase to spatially nonlocal perturbations and provides strong bounds on unitaries that rotate between states near solvable points in the code phase, with intriguing applications to condensed matter physics.