In characterization of quantum systems, adapting measurement settings based on data while it is collected can generally outperform in efficiency conventional measurements that are carried out independently of data. The existing methods for choosing measurement settings adaptively assume that the model, or the number of unknown parameters, is known. We introduce simultaneous adaptive model selection and parameter estimation. We apply our technique for characterization of a superconducting qubit and a bath of incoherent two-level systems, a leading decoherence mechanism in the state-of-the-art superconducting qubits.
In characterization of quantum systems, adapting measurement settings based on data while it is collected can generally outperform in efficiency conventional measurements that are carried out independently of data. The existing methods for choosing measurement settings adaptively assume that the model, or the number of unknown parameters, is known. We introduce simultaneous adaptive model selection and parameter estimation. We apply our technique for characterization of a superconducting qubit and a bath of incoherent two-level systems, a leading decoherence mechanism in the state-of-the-art superconducting qubits.
Two-level systems (TLS) in superconducting quantum devices are a dominant source of decoherence, noise, and device variability, ultimately limiting qubit performance and scalability. Efficient and reliable extraction of TLS parameters from spectroscopy measurements is therefore essential for both device characterization and materials optimization. In this thesis, machine learning methods are developed to accelerate and enhance TLS characterization from superconducting qubit spectroscopy data. The approach combines physics-based simulation of driven qubit–TLS dynamics with supervised learning models trained on synthetic datasets to infer underlying physical parameters from two-dimensional spectroscopy maps. Particular emphasis is placed on understanding how different parameters are encoded in observable features, and on evaluating the extent to which the inverse problem is well-posed. The results demonstrate that machine-learning-assisted inference can significantly reduce the computational cost of parameter estimation compared to conventional fitting-based approaches, while maintaining high accuracy for spectrally encoded parameters such as TLS frequency and coupling strength. In contrast, decoherence parameters are shown to be intrinsically more challenging to extract from short-time spectroscopy data, highlighting fundamental limitations of the measurement protocol rather than the learning model. Overall, this work establishes a data-driven framework for scalable TLS characterization and provides insight into the interplay between physical observability and machine learning-based inference in quantum systems.
Adaptive data collection and analysis, where data are being fed back to update the measurement settings, can greatly increase speed, precision, and reliability of the characterization of quantum systems. However, decoherence tends to make adaptive characterization difficult. As an example, we consider two coupled discrete quantum systems. When one of the systems can be controlled and measured, the standard method to characterize another, with an unknown frequency ${\ensuremath{\omega}}_{\mathrm{r}}$, is swap spectroscopy. Here, adapting measurements can provide estimates whose error decreases exponentially in the number of measurement shots rather than as a power law in conventional swap spectroscopy. However, when the decoherence time is so short that an excitation oscillating between the two systems can only undergo less than a few tens of vacuum Rabi oscillations, this approach can be marred by a severe limit on accuracy unless carefully designed. We adopt machine learning techniques to search for efficient policies for the characterization of decohering quantum systems. We find, for instance, that when the system undergoes more than 2 Rabi oscillations during its relaxation time T1,O(103) measurement shots are sufficient to reduce the squared error of the Bayesian initial prior of the unknown frequency ${\ensuremath{\omega}}_{\mathrm{r}}$ by a factor O(104) or larger. We also develop policies optimized for extreme initial parameter uncertainty and for the presence of imperfections in the readout.
We present an efficient method for the characterization of two coupled discrete quantum systems, one of which can be controlled and measured. For two systems with transition frequencies ωq, ωr, and coupling strength g we show how to obtain estimates of g and ωr whose error decreases exponentially in the number of measurement shots rather than as a power law expected in simple approaches. Our algorithm can thereby identify g and ωr simultaneously with high precision in a few hundred measurement shots. This is achieved by adapting measurement settings upon data as it is collected. We also introduce a method to eliminate erroneous estimates with small overhead. Our algorithm is robust against the presence of relaxation and typical noise. Our results are applicable to many candidate technologies for quantum computation, in particular, for the characterization of spurious two-level systems in superconducting qubits or stripline resonators.
In this work, we consider the fundamental task of estimating the purity of an unknown state to within multiplicative error ε. When one can perform general collective measurements, Θ(ε2d+εd) copies are known to be necessary and sufficient for this problem [AISW20]. However, implementing collective measurements on such a large number of copies can be experimentally demanding, and we thus aim to characterize the copy complexity of this problem with incoherent measurements.
In this setting, the only non-trivial result is a non-adaptive algorithm that uses O(ε2d+εd2) copies [PTTW26], which is polynomially larger than the best-known lower bound. Our first result is a new algorithm performing non-adaptive incoherent measurements that succeeds using O(ε2d+εd3/2) copies, improving on the latter term in the copy complexity. Moreover, we show that for any algorithm restricted to non-adaptive measurements, the above copy complexity is optimal.
We also develop a new adaptive estimator for the purity of a state that improves on the above complexity in the high-precision regime, i.e., for ε=o(1/d). We also show that the non-adaptive and adaptive estimators together yield the optimal complexity for incoherent purity estimation; in particular, we show that the copy complexity of this problem is Θ(min{ε2d+εd3/2,εd2+ε2d}).
The advancement and scaling of quantum technology has made the learning and identification of quantum systems and devices in highly multidimensional parameter spaces a pressing task for a variety of applications. In many cases, the integration of real-time feedback control and adaptive choice of measurement settings places strict demands on the speed of this task. Here we present a joint model selection and parameter estimation algorithm that is fast and operable on a large number of model parameters. The algorithm is based on variational Bayesian inference, which approximates the target posterior distribution by optimizing a tractable family of distributions, making it more scalable than exact inference methods relying on sampling and that generally suffer from high variance and computational cost in high-dimensional spaces. We show how a regularizing prior can be used to select between competing models, each comprising a different number of parameters, identifying the simplest model that explains the experimental data. The regularization can further separate the degrees of freedom, e.g., quantum systems in the environment or processes, which contribute to major features in the observed dynamics, with respect to others featuring small coupling, which only contribute to a background. As an application of the introduced framework, we consider the problem of the identification of multiple individual nuclear spins with a single electron spin quantum sensor, relevant for nanoscale nuclear magnetic resonance and for the implementation of multiqubit quantum networking nodes. With the number of environmental spins unknown a priori, our Bayesian approach is able to correctly identify the model, i.e., the number of spins and their couplings. We benchmark the algorithm on both simulated and experimental data, using standard figures of merit, and demonstrate that we can estimate dozens of parameters within minutes. Our methodology is compatible with the implementation of real-time adaptive choice of experimental settings in multiparameter estimation, which has the potential to greatly decrease the estimation time in a variety of metrology, tomography, and characterization tasks by prioritizing the measurements with the highest content of information.