Quantum entanglement is usually considered very fragile, because quantum systems tend to interact with the environment, which means that even at very low temperature, multi-particle entanglement is very hard to maintain.
In this study, we place such "folklore" under scrutiny by constructing local Hamiltonians for which any quantum state whose energy w.r.t. the Hamiltonian is at most, say 0.05 of the total available energy, is highly entangled, in a precise sense: the minimal depth circuits for generating any low-energy states must have depth at least logarithmic in the number of qubits.
This, in particular, answers a conjecture by Freedman and Hastings called NLTS, and in a way, removes a significant obstacle to achieving a quantum analog of the PCP theorem - namely local Hamiltonians whose ground-energy is QMA-hard to approximate even to, say, 0.05 fractional additive error.
In the talk, I'll assume no prior knowledge, so I'll describe the PCP and quantum PCP conjecture, the NLTS conjecture, and why previous works have actually indicated that it may be false.
Without diving into too much details, I'll give a taste of the intuition behind our construction, and why quantum codes prove extremely useful in this case.
Time allowing, I'll try to outline the next possible steps to be taken towards a more generalized and useful notion of "robust" quantum entanglement.
Joint work with Aram Harrow.
