Achievement

Energy calculations for bosons or fermions in N-particle states can be performed with two-particle reduced density matrices. Characterizing the set of two-particle reductions has worst cases that are hard to solve on a quantum computer. Efficient special-case approximation algorithms might exist because this set of reduced density matrices is convex. A related essential assumption (Erdahl's conjecture) is that every extreme point in this set is a reduction of a unique N-particle state.

Samuel Ocko (iQuISE Trainee), Xie Chen, and Beni Yoshida (iQuISE Associates) have disproved Erdahl’s conjecture [Phys. Rev. Lett. 106, 110501, (2011)], using two-body-interaction Hamiltonians with degenerate ground states -- quantum error corrections with unusual topologies -- that cannot be distinguished by two-body operators. Their work forges new links between quantum information, condensed matter physics, and quantum chemistry, and raises new questions about physically realizable quantum codes.