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

TL;DR

This paper emphasizes the importance of including circuit geometry, such as parasitic inductances and capacitances, in quantum circuit models to accurately account for electromagnetic noise, which affects quantum computing performance.

Contribution

It introduces a framework that incorporates circuit geometry into quantum circuit models, highlighting its impact on electromagnetic noise and quantum Hamiltonian complexity.

Findings

Geometry affects quantum circuit noise levels

Including parasitic elements improves model accuracy

High-frequency Hamiltonian components are challenging to simulate

Abstract

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.