  We propose a theory of characterizing quantum circuits with qubit functional
configurations. Any quantum circuit can be decomposed into alternating
sequences of 1-qubit unitary gates and CNOT gates. Each CNOT sequence prepares
the current quantum state into a layer of qubit functional configuration to
specify the rule for the next 1-qubit unitary sequence on how to collectively
modify the state vector entries. All the functional configuration layers on a
quantum circuit define its type which can include many other circuits sharing
the same configuration layers. Studying the functional configuration types
allows us to collectively characterize the properties and behaviors of many
quantum circuits. We demonstrate the theory's application to the
hardware-efficient ansatzes of variational quantum algorithms. For potential
applications, the functional configuration theory may allow systematic
understanding and development of quantum algorithms based on their functional
configuration types.
