NLTS Hamiltonians from Good Quantum Codes - Understanding Low-Energy States and Circuit Complexity

Watch a 42-minute colloquium talk from Harvard University's Anurag Anshu at the Centre for Quantum Technologies exploring the NLTS (No Low-Energy Trivial State) conjecture proposed by Freedman and Hastings in 2014. Delve into groundbreaking research that proves this conjecture by demonstrating how constant-rate and linear-distance Quantum LDPC codes correspond to NLTS local Hamiltonians. Learn about the conjecture's background, its significance in understanding many-body entanglement at high temperatures, and its connections to the quantum PCP conjecture. Gain insights into advanced proof techniques, including tools for proving quantum circuit lower bounds, while examining recent work that establishes fundamental principles in quantum computing and coding theory.