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arXiv:cond-mat/0512578 · New Journal of Physics

Decoherence from ensembles of two-level fluctuators

Josef Schriefl, Yuriy Makhlin, Alexander Shnirman, Gerd Schön

Published Jan 20, 2006• 252 citations
arXivHTMLPDF

Abstract

1/ f noise, the major source of dephasing in Josephson qubits, may be produced by an ensemble of two-level systems. Depending on the statistical properties of their distribution, the noise distribution can be Gaussian or non-Gaussian. The latter situation is realized, for instance, when the distribution of coupling strengths has a slowly decaying power-law tail. In this regime, questions of self-averaging and sample-to-sample fluctuations become crucial. We study the dephasing process for a class of distribution functions and analyse the self-averaging properties of the results.

DOI
10.1088/1367-2630/8/1/001

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1/ f noise, the major source of dephasing in Josephson qubits, may be produced by an ensemble of two-level systems. Depending on the statistical properties of their distribution, the noise distribution can be Gaussian or non-Gaussian. The latter situation is realized, for instance, when the distribution of coupling strengths has a slowly decaying power-law tail. In this regime, questions of self-averaging and sample-to-sample fluctuations become crucial. We study the dephasing process for a class of distribution functions and analyse the self-averaging properties of the results.
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
The efficiency of the future devices for quantum information processing will be limited mostly by the finite decoherence rates of the qubits. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, the noise that the quantum device demonstrates has a 1/ f spectrum. This suggests that the environment that destroys the phase coherence of the qubit can be thought of as a system of two-state fluctuators, which experience random hops between their states. In this short review, the current state of the theory of the decoherence due to the qubit interaction with the fluctuators is discussed. The effect of such an environment on two different protocols of the qubit manipulations, free induction and echo signal, is described. It turns out that in many important cases the noise produced by the fluctuators is non-Gaussian. Consequently, the results of the interaction of the qubit with the fluctuators are not determined by the pair correlation function alone. We describe the effect of the fluctuators using the so-called spin-fluctuator model. Being quite realistic, this model allows one to exactly evaluate the qubit dynamics in the presence of one fluctuator. This solution is found, and its features, including non-Gaussian effects, are analyzed in detail. We extend this consideration to systems of large numbers of fluctuators, which interact with the qubit and lead to the 1/ f noise. We discuss existing experiments on the Josephson qubit manipulation and try to identify non-Gaussian behavior.
Fluctuations of the qubit frequencies are one of the major problems to overcome on the way to scalable quantum computers. Of particular importance are fluctuations with a correlation time that exceeds the decoherence time due to decay and dephasing by fast processes. The statistics of the fluctuations can be characterized by measuring the correlators of the outcomes of periodically repeated Ramsey measurements. We describe qubit dynamics during repeated measurements and evaluate the two-time correlator for noise from two-level systems and two- and three-time correlators for Gaussian noise. The explicit expressions for the correlators are compared with simulations. We find that, even though the three-time correlators for noise from two-level systems and for Gaussian noise are generally significantly different, already ten two-level systems can mimic Gaussian noise provided they are symmetric. This is not the case for asymmetric systems.
Recent experiments by Yoshihara et al. [Phys. Rev. Lett. 97, 167001 (2006)] provided information on decoherence of the echo signal in Josephson-junction flux qubits at various bias conditions. These results were interpreted assuming a Gaussian model for the decoherence due to 1∕f1∕f1∕f noise. Here we revisit this problem on the basis of the exactly solvable spin-fluctuator model reproducing detailed properties of the 1∕f1∕f1∕f noise interacting with a qubit. We consider the time dependence of the echo signal and conclude that the results based on the Gaussian assumption need essential reconsideration.
We investigate the influence of nonstationary 1/ f μ noise, produced by interacting defects, on a quantum two-level system. Adopting a simple phenomenological model for this noise we describe exactly the corresponding dephasing in various regimes. The nonstationarity and pronounced non-Gaussian features of this noise induce new anomalous dephasing scenarii. Beyond a history-dependent critical coupling strength, the dephasing time exhibits a strong dependence on the age of the noise and the decay of coherence is not exponential.