Inferring charge-noise source locations from correlations in spin qubits

TL;DR

This work addresses the spatial localization of charge noise sources that limit spin-qubit devices. By analyzing cross-power spectral densities among two exchange-coupled qubits in isotopically purified Si/Si-Ge, the authors show that low-frequency noise is dominated by a small number of charge TLFs and demonstrate a triangulation method that uses cross-PSDs to infer TLF locations, validated by two experimentally identified TLFs with distinct switching times. They extend the approach to two-dimensional tilings and discuss extensions to larger qubit arrays and other qubit encodings, creating a general framework for pinpointing noise sources in scalable quantum processors. The findings have practical impact for noise mitigation and device engineering by enabling diagnostic localization of microscopic defects that degrade qubit performance.

Abstract

We investigate low-frequency noise in a spin-qubit device made in isotopically purified Si/Si-Ge. Observing sizable cross-correlations among energy fluctuations of different qubits, we conclude that these fluctuations are dominated by charge noise. At low frequencies, the noise spectra are not well described by a power law; instead, they reveal the presence of a few individual two-level fluctuators (TLFs). We demonstrate that the noise cross-correlations allow one to get information on the spatial location of such individual TLFs.

Figures (13)

• Figure 1: Image of a device identical to the one measured. Qubits, depicted as colored spheres with arrows, are formed under plunger gates PL and PR. The qubits are separated by distance $d$, have Zeeman energies $h\nu_L$ and $h\nu_R$, and interact via exchange $hJ$. The purple circle indicates the charge sensor.
• Figure 2: Schematics of a TLF located (a) left, (b) right, or (c) between two qubits. The left (right) qubit is shown as a blue (red) arrow in a circle, and the TLF as a dark orange star. A purple gradient marks increasing qubit energies to the right, with the black line indicating qubit separation. Faint colors show positions before the $|0\rangle \to |1\rangle$ TLF switch. Bottom panels display the resulting energy shifts and cross-PSD signs due to the TLF.
• Figure 3: Auto-PSDs of $S_L$ (blue), $S_R$ (red), and $S_J$ (yellow). Color gradients show Bayesian probability distributions Gutierrez-Rubio2022, with means as points. $S_J$ is shifted down by a factor 10 for clarity. The black dashed line is the model prediction from Eq. \ref{['eq:corr_exch']}. Gradient-colored fits of $S_L(f)$ and $S_R(f)$ use two Lorentzians $\propto [1+4\pi^2f^2\tau^2]^{-1}$ (see SM), with switching times $\tau=3.7$ s (green) and $\tau=90$ s (orange). A dotted line shows an $f^{-2}$ dependence for reference.
• Figure 4: Normalized cross-PSDs for the two-qubit system: $c_{LR}$ (purple), $c_{LJ}$ (green), and $c_{RJ}$ (orange). Magnitudes are shown in (a,c,e) and phases in (b,d,f). Color gradients give Bayesian probability distributions with means as points. Vertical dotted lines mark the frequency above which spectra are corrected for estimation errors (see SM); only the phase of $c_{LR}$ requires no correction. Black dashed lines are predictions from Eq. \ref{['eq:corr_exch']}. Schematics indicate the dominant TLF regime: right of the qubits at low frequencies, left at high, and a transition in between.
• Figure 5: TLF triangulation in two dimensions. (a) Regions with distinct cross-PSD signatures for a $3\times3$ qubit array (black circles). The tiling corresponds to a magnetic gradient $\nabla B_z \propto 1\hat{x} - 0.1 z \hat{z}$, similar to that of the device in Fig. \ref{['fig:device']}Rojas-Arias2023. Analogous tilings can be constructed for any known magnetic profile (or spin-orbit axis or $g$-tensor). (b) Contours of qubit-TLF interaction strength for a screened charge trap Rojas-Arias2023. Qubit wavefunctions are shown as Gaussian profiles (20 nm width). Dashed blue (red) lines denote contours of constant energy shifts for the left (right) qubit; solid lines match fitted jumps from PSD analysis ($|g^L|=14.9$ kHz, $|g^R|=38.0$ kHz, for the 90 s TLF). Intersections mark six candidate positions, with cross-PSD signs excluding the grey region and only leaving two possible locations (purple circles).