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arXiv:1507.02352 · Physical Review B

Non-Gaussian signatures and collective effects in charge noise affecting a dynamically decoupled qubit

Guy Ramon

Published Oct 16, 2015• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.92.155422

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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.
The efficiency of dynamical decoupling pulse sequences in removing noise due to a nearby charge fluctuator is studied for a singlet-triplet spin qubit. We develop a numerical method to solve the dynamical equations for all three components of the Bloch vector under a general pulse protocol, where pulses are applied along an arbitrary rotation axis. The qubit is shown to undergo both dephasing and dissipative dynamics, pending on its working position. Analytical solutions are found for the limits of weakly and strongly coupled fluctuators, shedding light on the distinct dynamics in the different parameter regimes. Scaling of the qubit decay time with the number of control pulses is found to follow a power law over a wide range of parameters and qubit bias points.
We study the dissipative dynamics of a qubit that is afflicted by classical random telegraph noise and is subject to dynamical decoupling. We derive exact formulas for the qubit dynamics at arbitrary working points in the limit of infinitely strong control pulses (bang-bang control), and we investigate in great detail the efficiency of the dynamical decoupling techniques for both Gaussian and non-Gaussian (slow) noise at qubit pure dephasing and at optimal point. We demonstrate that control sequences can be successfully implemented as diagnostic tools to infer spectral properties of a few fluctuators interacting with the qubit. The analysis is extended in order to include the effect of noise in the pulses, and we give upper bounds on the noise levels that can be tolerated in the pulses while still achieving an efficient dynamical decoupling performance.
We analyze theoretically the decoherence of two interacting electrons in a double self-assembled quantum dot due to a random telegraph noise. For this purpose we have examined the pure dephasing rate by evaluating the decoherence factor. The latter has been shown to be different from that calculated within the Gaussian approximation in the strong coupling regime. In order to determine the influence of the random telegraph noise on the entanglement of the system states, the concurrence, the populations, and the entropy are evaluated as well. Our results show that telegraph noise can severely impact the coherence of charge qubits.
In quantum computation, quantum coherence must be maintained during gate operation. However, in physical implementations, various couplings with the environment are unavoidable and can lead to a dephasing of a quantum bit (qubit). The background charge fluctuations are an important dephasing process, especially in a charge qubit system. We examined the dephasing rate of a qubit due to random telegraph noise. Solving stochastic differential equations, we obtained the dephasing rate of a qubit constructed of a coupled-dot system; we applied our results to the charge Josephson qubit system. We examined the dephasing rates due to two types of couplings between the coupled-dot system and the background charge, namely, fluctuation in the tunnel coupling constant and fluctuation in the asymmetric bias. For a strong-coupling condition, the dephasing rate was inversely proportional to the time constant of the telegraph noise. When there is fluctuation in the tunnel coupling constant, Gaussian decay occurs in the initial regime. We also examined the rate of dephasing due to many impurity sites. For a weak-coupling condition with fluctuation in the asymmetric bias, the obtained dephasing rate coincided with that obtained by the perturbation method using the spectral weight of a boson thermal bath, which is proportional to the inverse of the frequency.
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.
Many solid-state qubit systems are afflicted by low-frequency noise mechanisms that operate along two perpendicular axes of the Bloch sphere. Depending on the qubit control fields, either noise can be longitudinal or transverse to the quantization axis of the qubit, thus affecting its dynamics in distinct ways, generally contributing to decoherence that goes beyond pure dephasing. Here, we present a theory that provides a unified platform to study dynamics of a qubit subjected to two perpendicular low-frequency noises (assumed to be Gaussian and uncorrelated) under dynamical decoupling pulse sequences. The theory is demonstrated by the commonly encountered case of power law noise spectra, where approximate analytical results can be obtained.