NLTS Hamiltonians and Strongly-Explicit SoS Lower Bounds from Low-Rate Quantum LDPC Codes

Explore a 44-minute lecture on recent advancements in quantum complexity theory, focusing on NLTS Hamiltonians and Sum-of-Squares (SoS) lower bounds derived from low-rate quantum LDPC codes. Delve into Louis Golowich's presentation at the Simons Institute, where he discusses improvements to previous results in the field. Learn how quantum LDPC codes with arbitrarily small positive dimension can yield NLTS Hamiltonians, surpassing earlier findings. Discover a novel method for planting strongly explicit nontrivial codewords in linear-distance quantum LDPC codes, leading to strongly explicit SoS lower bounds. Gain insights into the potential applications of these "planted" quantum LDPC codes, which offer increased flexibility in code construction without relying on parity check counting.