  Optimal control of closed quantum systems is a well studied geometrically
elegant set of computational theory and techniques that have proven pivotal in
the implementation and understanding of quantum computers. The design of a
circuit itself corresponds to an optimal control problem of choosing the
appropriate set of gates (which appear as control operands) in order to steer a
qubit from an initial, easily prepared state, to one that is informative to the
user in some sense, for e.g., an oracle whose evaluation is part of the
circuit. However, contemporary devices are known to be noisy, and it is not
certain that a circuit will behave as intended. Yet, although the computational
tools exist in broader optimal control theory, robustness of adequate operation
of a quantum control system with respect to uncertainty and errors has not yet
been broadly studied in the literature. In this paper, we propose a new
approach inspired by the closed quantum optimal control and its connection to
geometric interpretations. To this end, we present the appropriate problem
definitions of robustness in the context of quantum control, focusing on its
broader implications for gate complexity.
