Dependence of quantum-fluctuation state selection on constraint implementation

Investigate which features of state selection by quantum fluctuations depend on the effective transition structure and which depend on the implementation of constraints in constrained quantum annealing and penalty-based quantum annealing.

Background

The paper establishes a correspondence between the leading effective Hamiltonians of penalty-based quantum annealing and constrained quantum annealing for cardinality-constrained graph bipartitioning. In the large-penalty regime, virtual single-spin flips in the penalty formulation generate an effective spin-exchange interaction proportional to the projected fully connected XY driver used directly in constrained quantum annealing.

Despite this correspondence, the authors leave unresolved the broader question of whether quantum-fluctuation-induced selection among degenerate ground states is governed primarily by the effective transition structure or by the manner in which the constraint is implemented. Resolving this issue could clarify when distinct constraint mechanisms produce the same sampling bias and when they favor different optimal configurations.