  Here we show that to quantize any lumped element circuit, the circuit
geometry must be included in a mathematical model of either the circuit fluxes
or the circuit charges. By geometry of the circuit, we refer to the so-called
parasitic inductances and capacitances that arise from the details of the
circuit layout, which are well known to create noise in classical circuits. In
contrast, the classical lumped element model describes only the topology of the
circuit, which defines how different finite element variables are connected to
one another by circuit components. By geometry we also refer to the fact that
the quantum variables define the circuit geometry - some are outside the wire,
some are inside the wire, and some are at boundary of the wire. Just as with
classical circuits, these effects create noise; this noise arises in the form
of high frequency components in the Hamiltonian that are difficult to
accurately simulate using a lumped element model. The presentation is
appropriate for undergraduate electrical and computer engineering students
learning about quantum computing and physicists learning about electrical
circuits.
