The Geometry of a Quantum Circuit and its Impact on Electromagnetic Noise

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.