NLTS conjecture

In quantum information theory, the no low-energy trivial state (NLTS) conjecture is a precursor to a quantum PCP theorem (qPCP) and posits the existence of families of Hamiltonians with all low-energy states of non-trivial complexity. It was formulated by Michael Freedman and Matthew Hastings in 2013. An NLTS proof would be a consequence of one aspect of qPCP problems – the inability to certify an approximation of local Hamiltonians via NP completeness. In other words, an NLTS proof would be one consequence of the QMA complexity of qPCP problems. On a high level, if proved, NLTS would be one property of the non-Newtonian complexity of quantum computation. NLTS and qPCP conjectures posit the near-infinite complexity involved in predicting the outcome of quantum systems with many interacting states. These calculations of complexity would have implications for quantum computing such as the stability of entangled states at higher temperatures, and the occurrence of entanglement in natural systems. There is currently a proof of NLTS conjecture published in preprint.