Gate-model quantum computer architectures represent an implementable model used to
realize quantum computations. The mathematical description of the dynamical attributes
of adaptive problem solving and iterative objective function evaluation in a gate-model
quantum computer is currently a challenge. Here, a mathematical model of adaptive
problem solving dynamics in a gate-model quantum computer is defined. We characterize
a canonical equation of adaptive objective function evaluation of computational problems.
We study the stability of adaptive problem solving in gate-model quantum computers.
