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arXiv:cond-mat/0312442 · Physical Review A

Dynamical suppression of telegraph and 1∕f noise due to quantum bistable fluctuators

G. Falci, Antonio D’Arrigo, Andrea Mastellone, Elisabetta Paladino

Published Oct 29, 2004• 85 citations
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Abstract

We study dynamical decoupling of a qubit from non-Gaussian quantum noise due to discrete sources, as bistable fluctuators and $1∕f$ noise. We obtain analytic and numerical results for generic operating points. For very large pulse frequency, where dynamic decoupling compensates decoherence, we found universal behavior. At intermediate frequencies noise can be compensated or enhanced, depending on the nature of the fluctuators and on the operating point. Our technique can be applied to a larger class of non-Gaussian environments.

DOI
10.1103/physreva.70.040101

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We study dynamical decoupling of a qubit from non-Gaussian quantum noise due to discrete sources, as bistable fluctuators and 1∕f1∕f1∕f noise. We obtain analytic and numerical results for generic operating points. For very large pulse frequency, where dynamic decoupling compensates decoherence, we found universal behavior. At intermediate frequencies noise can be compensated or enhanced, depending on the nature of the fluctuators and on the operating point. Our technique can be applied to a larger class of non-Gaussian environments.
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.
With the growing efforts in isolating solid-state qubits from external decoherence sources, the origins of noise inherent to the material start to play a relevant role. One representative example is charged impurities in the device material or substrate, which typically produce telegraph noise and can hence be modeled as bistable fluctuators. In order to demonstrate the possibility of the active suppression of the disturbance from a single fluctuator, we theoretically implement an elementary bang-bang control protocol, a protocol based on sudden pulses. We numerically simulate the random walk of the qubit state on the Bloch sphere with and without bang-bang compensation by means of a stochastic Schr\"odinger equation and compare it with an analytical saddle-point solution of the corresponding Langevin equation in the long-time limit. We find that the deviation with respect to the noiseless case is significantly reduced when bang-bang pulses are applied, being scaled down approximately by the ratio of the bang-bang period to the typical flipping time of the bistable fluctuation. Our analysis gives not only the effect of bang-bang control on the variance of these deviations, but also their entire distribution. As a result, we expect that bang-bang control works as a high-pass filter on the spectrum of noise sources. This indicates how the influence of 1∕f1∕f1∕f noise ubiquitous to the solid-state world can be reduced.
We investigate the capability of dynamical decoupling techniques to reduce decoherence from a realistic environment generating 1/f noise. The predominance of low frequency modes in the noise profile allows for decoherence scenarios where relatively slow control rates suffice for a drastic improvement. However, the actual figure of merit is very sensitive to the details of the dynamics, with decoupling performance which may deteriorate for non-Gaussian noise and/or high frequency working points. Our results are promising for robust solid-state qubits and beyond.
With the growing efforts in isolating solid-state qubits from external decoherence sources, the origins of noise inherent to the material start to play a relevant role. One representative example are charged impurities in the device material or substrate, which typically produce telegraph noise and can hence be modelled as bistable fluctuators. In order to demonstrate the possibility of the active suppression of the disturbance from a {\em single} fluctuator, we theoretically implement an elementary bang-bang control protocol. We numerically simulate the random walk of the qubit state on the Bloch sphere with and without bang-bang compensation by means of the stochastic Schrödinger equation and compare it with an analytical saddle point solution of the corresponding Langevin equation in the long-time limit. We find that the deviation with respect to the noiseless case is significantly reduced when bang-bang pulses are applied, being scaled down approximately by the ratio of the bang-bang period and the typical flipping time of the bistable fluctuation. Our analysis gives not only the effect of bang-bang control on the variance of these deviations, but also their entire distribution. As a result, we expect that bang-bang control works as a high-pass filter on the spectrum of noise sources. This indicates how the influence of 1/f1/f1/f-noise ubiquitous to the solid state world can be reduced.
Controlling the dynamics of entanglement and preventing its disappearance are central requisites for any implementation of quantum information processing. Solid state qubits are frequently affected by random telegraph noise due to bistable impurities of different nature coupled to the device. In this paper, we investigate the possibility to achieve an efficient universal two-qubit gate in the presence of random telegraph noise by periodic dynamical decoupling. We find an analytic form of the gate error as a function of the number of applied pulses valid when the gate time is much shorter then the telegraphic process correlation time. The analysis is further supplemented by exact numerical results demonstrating the feasibility of a highly-efficient universal two-qubit gate.
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.