Microscopic origin of low-frequency $1/f^{\alpha}$ charge noise in quantum-dot qubits in the few-fluctuator regime

Semiconductor quantum-dot qubits are limited by charge noise whose spectrum behaves as $1/f^{\alpha}$ with $\alpha \lesssim 1$ down to sub-Hertz frequencies, even though measurements indicate that each quantum dot is perturbed by only a small number of discrete two-level fluctuators (TLFs). The proposal that sub-bath temperature fluctuations in the two-dimensional electron gas (2DEG) modulate a few TLFs to generate the observed spectra was ruled out: thermal diffusion in a micrometer-scale 2DEG relaxes temperature fluctuations on nanosecond timescales, whereas $1/f$ noise at sub-Hz frequencies would require fluctuation lifetimes of seconds or longer. The surviving question is which microscopic mechanism — the identity of the fluctuating degrees of freedom and their dynamics — actually produces the observed decade-spanning low-frequency charge noise. No existing model resolves this: an interacting-TLF glass model gives qualitative agreement but does not identify the defects, and inference of fluctuator parameters from existing spectra is underdetermined.

Background

Charge noise is stochastic fluctuation of the electric potential felt by a qubit; in semiconductor spin qubits it dephases spins through the inevitable coupling of spin states to electric fields, and it is a principal obstacle to high-fidelity gates in silicon quantum-dot devices. Experimentally, the noise power spectral density in silicon/silicon-germanium (Si/SiGe) and silicon metal-oxide-semiconductor (SiMOS) quantum dots follows a $1/f^{\alpha}$ law ($\alpha \lesssim 1$) over many decades of frequency — up to nearly twelve decades in dynamically-decoupled exchange-oscillation measurements, in which pulse sequences make the qubit act as a frequency-selective noise filter while two spins oscillate via their tunable exchange coupling (Connors et al., Nat. Commun. 13, 940 (2022)) — and extends to millihertz frequencies (Connors et al., Phys. Rev. B 100, 165305 (2019)). A two-level fluctuator (TLF) is a microscopic entity that switches between two configurations (for example, a charge hopping between two trap sites); a single TLF with switching rate $\gamma$ contributes a Lorentzian spectrum, and the classical Dutta–Horn mechanism (Rev. Mod. Phys. 53, 497 (1981)) produces an approximate $1/f$ spectrum only from an ensemble of many TLFs with a broad, roughly uniform distribution of switching rates over the measured frequency window. This sits in tension with experiments indicating that an individual quantum dot is perturbed by only a few discrete fluctuators, each with its own activation energy. Ahn, Das Sarma, and Kestner (Phys. Rev. B 103, L041304 (2021)) proposed to reconcile the few-fluctuator observations with $1/f$ spectra by coupling a few thermally activated TLFs to a 'sub-bath' — a small region of the two-dimensional electron gas (2DEG, the conducting layer hosting the quantum dots) whose temperature undergoes significant statistical fluctuations; they showed this can yield $1/f$-like noise even from one or two TLFs and fits existing spectra. Mickelsen, Carruzzo, Coppersmith, and Yu (Phys. Rev. B 108, 075303 (2023)) tested this proposal with Monte Carlo simulations and analytic calculations of a two-state fluctuator with time-dependent switching rates: $1/f^{\alpha}$ noise at frequency $f_0$ requires the temperature fluctuations to persist for a time of order $1/f_0$. Estimating thermal relaxation by diffusion, with $f_{\min} = D/(\pi l^2)$ for the largest dimension $l$ of the 2DEG, gives a lowest fluctuation frequency of order GHz for a micrometer-scale Si/SiGe 2DEG — far above the sub-Hz regime where $1/f$ noise is observed. They note that such long-lived fluctuations generally require either a conservation law enforcing slow relaxation at large spatial scales (the mechanism Voss and Clarke examined for metal films, Phys. Rev. B 13, 556 (1976)) or some form of activated dynamics, neither of which is identified in the devices considered. Later work has sharpened but not resolved the question: Throckmorton and Das Sarma (Phys. Rev. B 109, 075304 (2024)) generalized the sub-bath model to a temperature-proportional 2DEG heat capacity without addressing the lifetime bound; Mickelsen, Carruzzo, and Yu (Phys. Rev. B 108, 195307 (2023)) proposed that a two-dimensional glass of interacting electric-dipole TLFs, coupled through the elastic strain field and modeled as a nearest-neighbor Ising spin glass, generates wandering switching rates and hence $1/f$-like spectra in qualitative agreement with experiment; Yoneda et al. (Nat. Phys. 19, 1793 (2023)) measured strong charge-noise correlation between qubits 100 nm apart; and Choi et al. (Phys. Rev. B 113, 094113 (2026)) showed that fluctuator positions, orientations, and strengths cannot be uniquely inferred from existing power-spectral-density data. None of these identifies the fluctuating entities or accounts quantitatively for the sub-Hz spectra.

Problem Statement

What is the microscopic origin of the low-frequency $1/f^{\alpha}$ charge noise ($\alpha \lesssim 1$) observed in semiconductor quantum-dot qubits down to sub-Hertz frequencies, in devices where the spectra and dynamics indicate that only a few discrete two-level fluctuators (TLFs) couple appreciably to each dot? An answer must (i) specify the fluctuating degrees of freedom — or an alternative noise-generation mechanism — and their dynamics; (ii) show quantitatively how the mechanism yields $1/f^{\alpha}$ spectra over the observed frequency range down to sub-Hz frequencies, including, if slow relaxation is invoked, fluctuation lifetimes $t_o \gtrsim 1/\omega_{\min}$ (where $\omega_{\min}$ is the lowest measured angular frequency and $t_o$ the lifetime of the underlying fluctuations) or another identified route to the required slow dynamics (for example, a long-range conserved quantity, activated dynamics, or rate wandering from interactions among fluctuators); and (iii) be consistent with the body of experimental constraints — the discreteness of few-fluctuator signatures, colored spectra over roughly twelve decades of frequency, dot-to-dot variability in magnitude and temperature dependence, noise correlations between qubits separated by ~100 nm, and the dependence of noise magnitude on gate-dielectric thickness and gate-stack materials. Temperature fluctuations of a diffusive 2DEG sub-bath are excluded by the analysis of Mickelsen et al. (2023); the question is what mechanism, if any, in fact operates.

References

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