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arXiv:1412.5536 · Physical Review B

Microscopic models for charge-noise-induced dephasing of solid-state qubits

Félix Beaudoin, W. A. Coish

Published Apr 29, 2015• 28 citations
arXivHTMLPDF

Abstract

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 ${T}_{2}$ 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 ${T}_{2}$ 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.

DOI
10.1103/physrevb.91.165432

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Several experiments have shown qubit coherence decay of the form exp[\ensuremath−(t/T2)\ensuremathα]exp[\ensuremath{-}{(t/{T}_{2})}^{\ensuremath{\alpha}}]exp[\ensuremath−(t/T2​)\ensuremathα] due to environmental charge-noise fluctuations. We present a microscopic description for temperature dependencies of the parameters T2{T}_{2}T2​ and \ensuremathα\ensuremath{\alpha}\ensuremathα. 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 \ensuremathα\ensuremath{\alpha}\ensuremathα 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.
The effects of a collection of classical two-level charge fluctuators on the coherence of a dynamically decoupled qubit are studied. Distinct dynamics is found at different qubit working positions. Exact analytical formulas are derived at pure dephasing and approximate solutions are found at the general working position, for weakly and strongly coupled fluctuators. Analysis of these solutions, combined with numerical simulations of the multiple random telegraph processes, reveal the scaling of the noise with the number of fluctuators and the number of control pulses, as well as dependence on other parameters of the qubit-fluctuators system. These results can be used to determine potential microscopic models for the charge environment by performing noise spectroscopy.
Low-frequency charge noise is a dominant source of decoherence in many solid-state qubit platforms. Conventionally, the noise is modeled as a bath of two-level fluctuators that activate or tunnel between minima in a potential energy landscape. Here, the authors describe measurements of charge noise in a superconducting qubit that suggest an unexpected dependence of the noise on the device scale. The measurements cannot be explained by the two-level fluctuate model. Rather, they are consistent with charge drift.
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.
Two level systems that can be reliably controlled and measured hold promise as qubits both for metrology and for quantum information science. Since a fluctuating environment limits the performance of qubits in both capacities, understanding environmental coupling and dynamics is key to improving qubit performance. We show measurements of the level splitting and dephasing due to the voltage noise of a GaAs singlet-triplet qubit during exchange oscillations. Unexpectedly, the voltage fluctuations are non-Markovian even at high frequencies and exhibit a strong temperature dependence. This finding has impacts beyond singlet-triplet qubits since nearly all solid state qubits suffer from some kind of charge noise. The magnitude of the fluctuations allows the qubit to be used as a charge sensor with a sensitivity of 2 × 10(-8)e/sqrt[Hz], 2 orders of magnitude better than a quantum-limited rf single electron transistor. Based on these measurements, we provide recommendations for improving qubit coherence, allowing for higher fidelity operations and improved charge sensitivity.
We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a non-ideal two level subspace, identified as the qubit and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model interaction we use can generate nonnegligible couplings between the qubit states and the higher levels upto N∼10N\sim 10N∼10. In contrast to the pure two-level system, in a multilevel system the quantum information may leak out of the qubit subspace through nonresonant as well as resonant excitations induced by the environment. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system's reduced density matrix. We numerically examine the relaxation and dephasing times as the environmental frequency spectrum, the environmental temperature, and the multilevel system parameters are varied. We observe the influence of all energy scales in the noise spectrum on the short time dynamics implying the dominance of nonresonant transitions at short times. The relaxation and dephasing times calculated, strongly depend on NNN for 4<N<104< N<104<N<10 and saturate for $10
We theoretically study the dephasing of an Andreev spin qubit (ASQ) due to electric and magnetic noise. Using a tight-binding model, we calculate the Andreev states formed in a Josephson junction where the link is a semiconductor with strong spin-orbit interaction. As a result of both the spin-orbit interaction and induced superconductivity, the local charge and spin of these states vary as a function of externally controllable parameters: the phase difference between the superconducting leads, an applied magnetic field, and filling of the underlying semiconductor. Concomitantly, coupling to fluctuations of the electric or magnetic environment will vary, which informs the rate of dephasing. We qualitatively predict the dependence of dephasing on the nature of the environment, magnetic field, phase difference between the junction, and filling of the semiconductor. Comparing the simulated electric- and magnetic-noise-induced dephasing rate to experiment suggests that the dominant source of noise is magnetic. Moreover, by appropriately tuning these external parameters, we find sweet spots at which we predict an enhancement in ASQ coherence times.