Abstract
The No low-energy trivial states (NLTS) conjecture — which posits the existence of a local Hamiltonian with a super-constant quantum circuit lower bound on the complexity of all low-energy states — is a fundamental unresolved obstacle to a positive resolution of the quantum PCP conjecture. In this talk, we elucidate the connection between these two unresolved conjectures as well as discuss progress [Anshu & Nirkhe 2020] towards the positive resolution of the NLTS conjecture. This will explore connections between notions of quantum error correction and the robustness of entanglement. The talk will conclude with a discussion on strategies towards proving the quantum PCP conjecture.