Alternative generalizations for slack-variable initialization and drivers in the standard adiabatic algorithm

Develop and analyze alternative choices of initial states and driver Hamiltonians for slack variables encoded as qudits or oscillators when enforcing inequality constraints in the standard adiabatic algorithm, beyond initializing to uniform superpositions and using projectors onto these states.

Background

To handle inequality constraints, the authors introduce slack variables and discuss initializing them to uniform superpositions with corresponding projectors in the driver Hamiltonian, extending the usual qubit-only approach. They note that different generalizations for qudits and infinite-dimensional modes may be preferable.

They explicitly leave the design and evaluation of such alternatives to future work.