NLTS Hamiltonians from good quantum codes
CQT Colloquium
Speaker: Anurag Anshu, Harvard University
Abstract:The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist local Hamiltonians with all low energy states of non-trivial complexity (with complexity measured by the quantum circuit depth preparing the state). Our recent work https://ddec1-0-en-ctp.trendmicro.com... (with Nikolas Breuckmann and Chinmay Nirkhe) proves this conjecture by showing that the recently discovered families of constant-rate and linear-distance Quantum LDPC codes correspond to NLTS local Hamiltonians. This talk will provide background on the conjecture, its relevance to many-body entanglement at high temperatures and connections with quantum PCP conjecture. We will also touch upon the proof techniques, such as the tools needed to prove quantum circuit lower bounds.