  A computational problem fed into a gate-model quantum computer identifies an
objective function with a particular computational pathway (objective function
connectivity). The solution of the computational problem involves identifying a
target objective function value that is the subject to be reached. A bottleneck
in a gate-model quantum computer is the requirement of several rounds of
quantum state preparations, high-cost run sequences, and multiple rounds of
measurements to determine a target (optimal) state of the quantum computer that
achieves the target objective function value. Here, we define a method for
optimal quantum state determination and computational path evaluation for
gate-model quantum computers. We prove a state determination method that finds
a target system state for a quantum computer at a given target objective
function value. The computational pathway evaluation procedure sets the
connectivity of the objective function in the target system state on a fixed
hardware architecture of the quantum computer. The proposed solution evolves
the target system state without requiring the preparation of intermediate
states between the initial and target states of the quantum computer. Our
method avoids high-cost system state preparations and expensive running
procedures and measurement apparatuses in gate-model quantum computers. The
results are convenient for gate-model quantum computations and the near-term
quantum devices of the quantum Internet.
