  Superconducting quantum circuits are a promising hardware platform for
realizing a fault-tolerant quantum computer. Accelerating progress in this
field of research demands general approaches and computational tools to analyze
and design more complex superconducting circuits. We develop a framework to
systematically construct a superconducting quantum circuit's quantized
Hamiltonian from its physical description. As is often the case with quantum
descriptions of multicoordinate systems, the complexity rises rapidly with the
number of variables. Therefore, we introduce a set of coordinate
transformations with which we can find bases to diagonalize the Hamiltonian
efficiently. Furthermore, we broaden our framework's scope to calculate the
circuit's key properties required for optimizing and discovering novel qubits.
We implement the methods described in this work in an open-source Python
package SQcircuit. In this manuscript, we introduce the reader to the SQcircuit
environment and functionality. We show through a series of examples how to
analyze a number of interesting quantum circuits and obtain features such as
the spectrum, coherence times, transition matrix elements, coupling operators,
and the phase coordinate representation of eigenfunctions.
