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 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.

Наука