Fast, accurate, and error-resilient variational quantum noise spectroscopy

Abstract: Detecting and characterizing decoherence-inducing noise sources is critical for developing scalable quantum technologies and deploying quantum sensors that operate at molecular scales. Yet, existing methods for such noise spectroscopy face fundamental difficulties, including their reliance on severe approximations and the need for extensively averaged measurements. Here, we propose an alternative approach that processes the commonly performed dynamical decoupling-based coherence measurements using a novel self-consistent optimization framework to extract the noise power spectrum that characterizes the interaction between a qubit or quantum sensor and its environment. Our approach adopts minimal assumptions and is robust to the presence of measurement errors. We introduce a protocol to quantify confidence intervals and a physically motivated heuristic to determine which new dynamical decoupling measurement can improve spectral reconstruction. We employ our method to reconstruct the noise spectrum of a nitrogen-vacancy sensor in diamond, resolving previously undetected nuclear species at the diamond surface and revealing that the previous measurements of low-frequency noise had overestimated its strength by an order of magnitude. Our method's noise spectrum reconstructions uncover previously unsuspected structure and offer unprecedented accuracy, setting the stage for precision noise spectroscopy-based quantum metrology.