Flux noise and dephasing in superconducting flux qubits

Short answer: For many types of superconducting qubits, magnetic flux noise is a source of pure dephasing. A 2012 Physical Review B paper measured flux noise in a dc SQUID that follows a power law, with the spectral density scaling as 1/f to the power alpha and alpha between 0.61 and 0.95. It also calculates how the pure dephasing time depends on that exponent. Later work reports a classical-quantum crossover of 1/f flux noise. These are measurements on individual devices, and the exponent differs between studies.

What the noise looks like

The 2012 paper reports measurements on a representative dc superconducting quantum interference device (SQUID) over a range of temperatures. The flux noise spectral density follows S(f) = A squared divided by (f / 1 Hz) to the power alpha, with A of the order of 1 micro flux quantum per root hertz and 0.61 <= alpha <= 0.95. A 2006 paper from a RIKEN group investigates decoherence in Josephson-junction flux qubits. By measuring decoherence at various bias conditions, the authors separate the contributions of different noise sources, and they present a Gaussian decay function extracted from the echo signal as evidence of dephasing due to 1/f flux noise.

Effect on dephasing time

For a qubit whose energy level splitting is linearly coupled to the applied flux, the 2012 paper calculates the pure dephasing time for Ramsey and echo pulse sequences. Its abstract says the dephasing time depends strongly on alpha and decreases rapidly as alpha is reduced. The paper also compares the ratio of echo to Ramsey dephasing times, which depends on alpha and on the noise bandwidth. The sensitivity of these times to the pivot frequency, where the spectral density is fixed at about 1 Hz, is also analysed.

A classical-quantum crossover

A 2017 Physical Review Letters paper analyses the dissipative dynamics of a tunable gap flux qubit and extracts both sides of the two-sided flux noise spectral density over a range of frequencies around 2kT/h of about 1 GHz, which lets the authors observe a classical-quantum crossover. Below the crossover point the symmetric noise component follows a 1/f power law that matches the magnitude of the 1/f noise near 1 Hz. The antisymmetric component shows a 1/T dependence below 100 mK, which the authors call dynamical evidence for a paramagnetic environment. They say extrapolating the two-sided spectrum predicts the linewidth and reorganisation energy of incoherent resonant tunnelling between flux qubit wells.

Limits

The three papers study different devices, from a SQUID to flux qubits, and report different exponents and conditions. They describe the noise, not a method that removes it, and they do not give a single value that applies to every qubit.

FAQ

What does flux noise do to a qubit?

For many types of superconducting qubits it is a source of pure dephasing, per the 2012 paper.

Is the exponent always 1?

No. The 2012 SQUID measurements found alpha from 0.61 to 0.95, while the 2006 paper interprets its echo data as 1/f noise.

Does an echo sequence help?

The 2012 paper compares echo and Ramsey dephasing times and finds the ratio depends on alpha and the noise bandwidth.

What is the classical-quantum crossover?

A 2017 paper observes the flux noise spectrum change character around 2kT/h of about 1 GHz, with the symmetric part following 1/f below it.

What does the 1/T dependence indicate?

The 2017 authors say the antisymmetric noise component's 1/T dependence below 100 mK is dynamical evidence for a paramagnetic environment.