Qubit noise spectroscopy (QNS) is a valuable tool for both the characterization of a qubit’s environment and as a precursor to more effective qubit control to improve qubit fidelities. Existing approaches to QNS are what the classical spectrum estimation literature would call “nonparametric” approaches, in that a series of probe sequences are used to estimate noise power at a set of points or bands. In contrast, model-based approaches to spectrum estimation assume additional structure in the form of the spectrum and leverage this for improved statistical accuracy or other capabilities, such as superresolution. Here, we derive model-based QNS approaches using inspiration from classical signal processing, primarily through the recently developed Schrödinger wave autoregressive moving-average formalism for modeling correlated noise. We show, through both simulation and experimental data, how these model-based QNS approaches maintain the statistical and computational benefits of their classical counterparts, resulting in powerful estimation approaches. Beyond the direct application of these approaches to QNS and quantum sensing, we anticipate that the flexibility of the underlying models will find utility in adaptive feedback control for quantum systems, in analogy with their role in classical adaptive signal processing and control.

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• Noise
• Open quantum systems & decoherence
• Quantum control
• Quantum information with solid state qubits
• Quantum protocols
• Superconducting qubits
• Microwave techniques
• Time series analysis