  Quantum annealing is a novel type of analog computation that aims to use
quantum mechanical fluctuations to search for optimal solutions of Ising
problems. Quantum annealing in the transverse field Ising model, implemented on
D-Wave devices, works by applying a time dependent transverse field, which puts
all qubits into a uniform state of superposition, and then applying a
Hamiltonian over time which describes a user programmed Ising problem. We
present a method which utilizes two control features of D-Wave quantum
annealers, reverse annealing and an h-gain schedule, to quantify the
susceptibility, or the distance, between two classical states of an Ising
problem. The starting state is encoded using reverse annealing, and the second
state is encoded on the linear terms of problem Hamiltonian. An h-gain schedule
is specified which incrementally increases the strength of the linear terms,
thus allowing a quantification of the h-gain strength required to transition
the anneal into a specific state at the final measurement. By the nature of
quantum annealing, the state tends towards global minima and therefore we
restrict the second classical state to a minimum solution of the given Ising
problem. This susceptibility mapping, when enumerated across all initial
states, shows in detail the behavior of the quantum annealer during reverse
annealing. The procedure is experimentally demonstrated on three small test
Ising's which were embedded in parallel on the D-Wave Advantage_system4.1.
Analysis of the state transition mapping shows detailed characteristics of the
reverse annealing process including intermediate state transition paths, which
are visually represented as state transition networks.
