Entangling Problem Hamiltonian for Adiabatic Quantum Computation

Adiabatic quantum computation starts from embedding a computational problem into Hamiltonian whose ground state encodes the solution to problem. This is normally chosen be diagonal in basis, that product basis for qubits. We demonstrate that, fact, can always non-diagonal basis. To more precise, we show how construct such way all its excited states are entangled with respect qubit tensor structure, while still of form and conjecture entangling Hamiltonians might evade many-body localization bottleneck adiabatic thus improve performance.