Spin Lock Noise Spectroscopy

[jevillegasd]

The idea would be to implement a noise spectroscopy routine based on rotating-frame relaxation ($T_{1\rho}$) to characterize high-frequency environmental noise acting on the qubits during driven evolution, complementing existing free-evolution routines (Ramsey, Hahn-Echo). A version of this was presented by Tatiana some time ago and used to measure noise in the 20Q QPU.

Reference issue (for implementation): #1527

Background

Some references are Yan & Oliver (2013) and Yan & Oliver (2016)

Standard continuous-driving Rabi experiments are vulnerable to low-frequency 1/f drifts, causing artifacts in noise reconstruction. By employing a spin-locking sequence, the qubit state is locked parallel to the driving field in the rotating frame. This shifts the decoherence mechanism to longitudinal relaxation ($T_{1\rho}$), filtering out low-frequency phase noise and allowing clean mapping of the noise power spectral density (PSD) at the Rabi frequency $\nu_R$. This is critical for detecting coherent microscopic two-level system (TLS) defects.

Proposed Pulse Sequence Implementation

The basic implementation folows:

• Preparation: Apply a resonant $\pi/2$ pulse along the $Y$-axis to bring the qubit state to the equator (aligned with the $X$-axis).
• Spin-Lock: Apply a continuous driving field along the $X$-axis (phase-shifted by $90^\circ$ relative to the first pulse) for a variable duration $\tau$. The drive amplitude dictates the target spectroscopy frequency $\nu_R$. The Rabi frequency can be calculate scaling from the pi pulse value.
• Back-Projection: Apply an additional $\pi/2$ pulse along the $Y$ axis to project for $Z$-axis readout.

To prevent state oscillations caused by phase diffusion during unavoidable inter-pulse gaps, the paper suggests variants (SL-5 a/b)

Expected Parameters and Outputs

• Sweep Parameters: Spin-lock duration ($\tau$) and driving amplitude (Rabi frequency $\nu_R$).
• Fits & Plots:Exponential decay fits of qubit population vs. $\tau$ to extract the relaxation rate $\Gamma_{1\rho}(\nu_R)$.
• A final profile mapping the Noise Power Spectral Density $S(\nu_R)$ vs. Frequency ($\nu_R$), exposing flat backgrounds, 1/f lines, and local TLS defect peaks.

Next

Running this spectroscopy for different resonator populations can be used to characterize the sensitivity of the qubit to noise in the feedline / RO resonator (which was the use case presented by Tatiana)

[alecandido]

I believe this was a good proposal, detailed enough to be an issue on its own, no doubt (then, I'm not saying anything about priority 😬).

Since it was turned into #1527, I would move there all the discussion. Thanks @jevillegasd!