  In a typical quantum annealing protocol, the system starts with a transverse
field Hamiltonian which is gradually turned off and replaced by a longitudinal
Ising Hamiltonian. The ground state of the Ising Hamiltonian encodes the
solution to the computational problem of interest, and the state overlap with
this ground state gives the success probability of the annealing protocol. The
form of the annealing schedule can have a significant impact on the ground
state overlap at the end of the anneal, so precise control over these annealing
schedules can be a powerful tool for increasing success probabilities of
annealing protocols. Here we show how superconducting circuits, in particular
capacitively shunted flux qubits (CSFQs), can be used to construct quantum
annealing systems by providing tools for mapping circuit flux biases to Pauli
coefficients. We use this mapping to find customized annealing schedules:
appropriate circuit control biases that yield a desired annealing schedule,
while accounting for the physical limitations of the circuitry. We then provide
examples and proposals that utilize this capability to improve quantum
annealing performance.
