Ground state connectivity of local Hamiltonians

Understand

The study of ground state energies of local Hamiltonians has played a fundamental role in quantum complexity theory.

• In this paper, we take a new direction by introducing the physically motivated notion of "ground state connectivity" of local Hamiltonians, which captures problems in areas ranging from quantum stabilizer codes to quantum memories.
• Roughly, "ground state connectivity" corresponds to the natural question: Given two ground states |{\psi}> and |{\phi}> of a local Hamiltonian H, is there an "energy barrier" (with respect to H) along any sequence of local operations mapping |{\psi}> to |{\phi}>? We show that the complexity of this question can range from QCMA-complete to PSPACE-complete, as well as NEXP-complete for an appropriately defined "succinct" version of the problem.
• As a result, we obtain a natural QCMA-complete problem, a goal which has generally proven difficult since the conception of QCMA over a decade ago.