The AHP Prize 2017 was awarded to Johannes Bausch, Toby Cubitt, and Maris Ozols for the paper
The investigations of quantum Hamiltonian complexity belong to the hottest, but also to the most dffcult and challenging subjects of the contemporary quantum information theory.
They concern mathematics, physics, computer science and even quantum technologies. In simple words the question is the following: assuming we have access to a universal quantum computer, how hard is it to compute the ground state energy, or the energy gap for a class of physically relevant Hamiltonians?
Bausch, Cubitt and Ozols show rigorously that "estimating the ground state energy of a translationally invariant, nearest-neighbour Hamiltonian on a 1D spin chain" is extremely hard, and belong to the class of, so called, Quantum-Merlin-ArthurEXP complete problems, even for systems of low local dimension (spins of order ≈ 40).
This is an improvement over the best previously known result by several orders of magnitude, and it leads to an amazing and surprising conclusion "that spin-glass-like frustration can occur in translation invariant quantum systems with a local dimension comparable to the smallest-known nontranslation invariant systems with similar behaviour."