Decoherence induced by a sparse bath of two-level fluctuators: Peculiar features of 1 / f noise in high-quality qubits

Abstract

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