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arXiv:2007.03689 · Physical review. B./Physical review. B

Microscopic bath effects on noise spectra in semiconductor quantum dot qubits

Seongjin Ahn, S. Das Sarma, J. P. Kestner

Published Jan 25, 2021• 18 citations
arXivHTMLPDF

Abstract

When a system is thermally coupled to only a small part of a larger bath, statistical fluctuations of the temperature (more precisely, the internal energy) of this ``sub-bath'' around the mean temperature defined by the larger bath can become significant. We show that these temperature fluctuations generally give rise to $1/f$-like noise power spectral density from even a single two-level system. We extend these results to a distribution of fluctuators, finding the corresponding modification to the Dutta-Horn relation. Then we consider the specific situation of charge noise in silicon quantum dot qubits and show that recent experimental data [E. J. Connors et al., Phys. Rev. B 100, 165305 (2019)] can be modeled as arising from as few as two two-level fluctuators, and accounting for sub-bath size improves the quality of the fit.

DOI
10.1103/physrevb.103.l041304

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When a system is thermally coupled to only a small part of a larger bath, statistical fluctuations of the temperature (more precisely, the internal energy) of this ``sub-bath'' around the mean temperature defined by the larger bath can become significant. We show that these temperature fluctuations generally give rise to 1/f1/f1/f-like noise power spectral density from even a single two-level system. We extend these results to a distribution of fluctuators, finding the corresponding modification to the Dutta-Horn relation. Then we consider the specific situation of charge noise in silicon quantum dot qubits and show that recent experimental data [E. J. Connors et al., Phys. Rev. B 100, 165305 (2019)] can be modeled as arising from as few as two two-level fluctuators, and accounting for sub-bath size improves the quality of the fit.
Progress in fabrication of semiconductor and superconductor qubits has greatly diminished the number of decohering defects, thus decreasing the devastating low-frequency 1 / f noise and extending the qubits' coherence times (dephasing time T 2 * and the echo decay time T 2 ). However, large qubit-to-qubit variation of the coherence properties remains a problem, making it difficult to produce a large-scale register where all qubits have a uniformly high quality. In this work, we show that large variability is a characteristic feature of a qubit dephased by a sparse bath made of many ( n ≫ 1 ) decohering defects, coupled to the qubit with similar strength. We model the defects as two-level fluctuators (TLFs) whose transition rates γ are sampled from a log-uniform distribution over an interval [ γ m , γ M ] , which is a standard model for 1 / f noise. We investigate decoherence by such a bath in the limit of high-quality qubit, i.e., when the TLF density d is small (the limit of sparse bath, with d = n / w ≪ 1 , where n is the number of TLFs and w = ln [ γ M / γ m ] is the log-width of the distribution). We show that different realizations of the bath produce very similar noise power spectra S ( f ) ∼ 1 / f , but lead to drastically different coherence times T 2 * and T 2 . Thus the spectral density S ( f ) does not determine coherence of a qubit coupled to a sparse TLF bath, as opposed to a dense bath; instead, decoherence is controlled by only a few exceptional fluctuators, determined by their value of γ . We show that removing only two of these TLFs greatly increases T 2 and T 2 * times. Our findings help theoretical understanding and further improvements in the coherence properties of semiconductor and superconductor qubits, battling the 1 / f noise in these platforms. Published by the American Physical Society 2024
Several experiments have shown qubit coherence decay of the form $exp[\ensuremath{-}{(t/{T}_{2})}^{\ensuremath{\alpha}}]$ due to environmental charge-noise fluctuations. We present a microscopic description for temperature dependencies of the parameters T2{T}_{2}T2​ and $\ensuremath{\alpha}$. Our description is appropriate to qubits in semiconductors interacting with spurious two-level charge fluctuators coupled to a thermal bath. We find distinct power-law dependencies of T2{T}_{2}T2​ and $\ensuremath{\alpha}$ on temperature depending on the nature of the interaction of the fluctuators with the associated bath. We consider fluctuator dynamics induced by first- and second-order tunneling with a continuum of delocalized electron states. We also study one- and two-phonon processes for fluctuators in either GaAs or Si. These results can be used to identify dominant charge-dephasing mechanisms and suppress them.
Cross-correlated charge noise in silicon quantum dots has emerged as an important issue for fault-tolerant quantum computation, as it has been suggested to both limit quantum error correction performance and reveal unique information about noise sources. We develop a method to characterize charge noise cross-correlations in a semiconductor qubit device based solely on quantum-dot transport current. By dynamically switching the site-selective sensitivity of transport current through a double quantum dot to charge noise, we extract potential fluctuations at individual dots without requiring additional sensing devices or spin operations. Based on the obtained power spectral densities, we discuss the coupling of a dominant two-level fluctuator to individual dots. We furthermore verify the consistency of the measurement protocol by applying artificial noise via gate electrodes and investigate the temperature dependence of charge noise correlations. The method offers a convenient and versatile alternative approach that substantially facilitates the assessment of charge noise correlations in diverse semiconductor qubit devices.
Correlated noise across multiqubit architectures is known to be highly detrimental to the operation of error-correcting codes and the long-term feasibility of quantum processors. The recent discovery of spatially dependent correlated noise in multiqubit architectures of superconducting qubits arising from the impact of cosmic radiation and high-energy particles giving rise to quasiparticle poisoning within the substrate has led to intense investigations of mitigation strategies to address this. Correlated noise in semiconductor spin qubits is also now receiving attention, as this platform begins to scale. Here we report the magnitude, frequency, and spatial dependence of noise correlations between four silicon quantum dot pairs as a function of interdot distance at frequencies from 0.3 to 1 mHz. We find the magnitude of charge-noise correlations, quantified by the magnitude square coherence C x y , are significantly suppressed from > 0.5 to < 0.1 as the interdot distance increases from 75 to 300 nm. Using an analytical model we confirm that, in contrast to superconducting qubits, the dominant source of correlated noise arises from low-frequency charge noise from the presence of two level fluctuators (TLFs) at the native silicon-silicon dioxide surface. Knowing this, we conclude with a timely discussion of charge-noise mitigation strategies.
Discrete charge fluctuations, routinely observed in semiconductor quantum dot devices, may contribute significantly to device drift and errors resulting from qubit miscalibration. Understanding the nature and origins of these discrete charge fluctuations may provide insights into material improvements or means of mitigating charge noise in semiconductor quantum dot devices. In this work, we measure multi-level charge fluctuations present in a Si/SiGe double quantum dot device over a range of device operating voltages and temperatures. To characterize the parameter-dependent dynamics of the underlying fluctuating degrees of freedom, we perform a detailed analysis of the measured noise timeseries. We perform algorithmically assisted drift detection and change point detection to detrend the data and remove a slow fluctuator component, as a preprocessing step. We perform model comparison on the post-processed time series between different nnn-level fluctuator (nnnLF) factorial hidden Markov models (FHMMs), finding that although at most sweep values the independent pair of 2LFs model would be preferred, in a particular region of voltage space the 4LF model outperforms the other models, indicating a conditional rate dependence between the two fluctuators. By tracking fluctuator transition rates, biases, and weights over a range of different device configurations, we estimate gate voltage and conductivity sensitivity. In particular, we fit a phenomenological, detailed balance model to the extracted independent 2LFs rate data, yielding lever arm estimates in the range of −2μ-2 μ−2μeV/mV up to 4μ4 μ4μeV/mV between the two 2LFs and nearby gate electrodes. We expect that these characterization results may aid in subsequent spatial triangulation of the charge fluctuators.
Charge noise is an important factor limiting qubit coherence and relaxation in solid-state devices. In bilayer graphene (BLG) quantum dots, recently established as a promising platform for spin- and valley-based qubits, both the origin and magnitude of charge noise remain largely unexplored. Here, we investigate high-frequency charge noise using Landau-Zener-Stückelberg-Majorana (LZSM) interference spectroscopy. We study a single-particle charge qubit formed in a BLG double quantum dot at frequencies between 5 and 10 GHz and extract a noise spectral density SεS_\varepsilonSε​ on the order of 0.5-0.9 neV/Hz/\sqrt{\mathrm{Hz}}/Hz​. This is comparable to values reported for III-V semiconductor platforms and silicon. From the temperature and frequency dependence of the charge qubit decoherence, we conclude that thermal (Johnson) noise or electron-phonon coupling dominates over two-level fluctuators.