# Flux noise in a superconducting transmission line

## TL;DR

This paper investigates flux noise in superconducting transmission lines caused by random magnetization, analyzing its effects on flux correlations and implications for qubit relaxation and voltage noise.

## Contribution

It models low-frequency flux noise in superconducting TLs using diffusion equations and evaluates flux-flux correlations considering non-local effects.

## Key findings

- Flux noise increases faster than line length.
- Frequency dispersion occurs around inverse diffusion time.
- Flux-flux correlation can be measured via qubit relaxation and voltage noise.

## Abstract

We study a superconducting transmission line (TL) formed by distributed LC oscillators and excited by external magnetic fluxes which are aroused from random magnetization (A) placed in substrate or (B) distributed at interfaces of a two-wire TL. Low-frequency dynamics of a random magnetic field is described based on the diffusion Langevin equation with a short-range source caused by (a) random amplitude or (b) gradient of magnetization. For a TL modeled as a two-port network with open and shorted ends, the effective magnetic flux at the open end has non-local dependency on noise distribution along the TL. The flux-flux correlation function is evaluated and analyzed for the regimes (Aa), (Ab). (Ba), and (Bb). Essential frequency dispersion takes place around the inverse diffusion time of random flux along the TL. Typically, noise effect increases with size faster than the area of TL. The flux-flux correlator can be verified both via the population relaxation rate of the qubit, which is formed by the Josephson junction shunted by the TL with flux noises, and via random voltage at the open end of the TL.