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 T₂^* and the echo decay time T₂). 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 [γₘ,γM], 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[γM/γₘ] 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 T₂^* and T₂. 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 T₂ and T₂^* 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.
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Mehmandoost et al. (2024) studied this question.