NLTS conjecture

<p>In <a href="/facts/Quantum_information/Bl9QIvHj">quantum information theory</a>, the no low-energy trivial state (NLTS) conjecture is a precursor to a <a href="/facts/Quantum_PCP_conjecture/GwlBcYH6">quantum PCP theorem</a> (qPCP) and posits the existence of families of <a href="/facts/Hamiltonian_(quantum_mechanics)/5XwK2HmD">Hamiltonians</a> with all <a href="/facts/Energy_level/66x51Khc">low-energy states</a> of <a href="/facts/Computational_complexity/Qenh22Ja">non-trivial complexity</a>. It was formulated by <a href="/facts/Michael_Freedman/FxESCuA7">Michael Freedman</a> and <a href="/facts/Matthew_Hastings/Nfn5qb4n">Matthew Hastings</a> in 2013. NLTS is a consequence of one aspect of qPCP problems –  the inability to <a href="/facts/Certificate_(complexity)/6hC8dfSt">certify</a> an approximation of local Hamiltonians via <a href="/facts/NP_completeness/NFPv56DU">NP completeness</a>. In other words, it is a consequence of the <a href="/facts/QMA/AtQsb09s">QMA</a> complexity of qPCP problems. On a high level, it is one property of the non-<a href="/facts/Classical_mechanics/ykG8upsN">Newtonian</a> complexity of <a href="/facts/Quantum_computing/nbbcgmvq">quantum computation</a>. 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 <a href="/facts/Quantum_entanglement/afzslwN0">entangled</a> states at higher <a href="/facts/Temperature/QyGe4gmj">temperatures</a>, and the occurrence of entanglement in natural systems. A proof of the NLTS conjecture was presented and published as part of <a href="/facts/Symposium_on_Theory_of_Computing/xsemn7kG">STOC</a> 2023.
</p>

NLTS conjecture open-in-new

NLTS conjecture