Robust Online Hamiltonian Learning (1207.1655v2)

Abstract: In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance.

Robust Online Hamiltonian Learning

The paper "Robust Online Hamiltonian Learning" presents a novel algorithmic framework that aims to infer dynamical parameters of quantum systems by fusing techniques from sequential Monte Carlo (SMC) methods and Bayesian experimental design. This synthesis provides a robust mechanism for accurately estimating Hamiltonian parameters in scenarios characterized by significant variability and noise.

Overview and Methodology

The authors introduce an approach designed to operate online during experimental data collection, circumventing the need for storage and off-line post-processing of large data sets. By leveraging SMC techniques, the algorithm captures the parameter space as a distribution supported over a set of particles, with weights evolving through Bayesian updates. The core innovation lies in adaptive experiment design, realized through Bayesian experimental design principles. This involves selecting control parameters dynamically during the experiment, optimizing informational gain relative to the unknown parameters.

Additionally, the algorithm effectively manages the trade-offs between computational complexity and experimental efficacy, allowing practical implementation even in resource-constrained environments. The provision for hyperparameter estimation—learning distributions describing fluctuations in Hamiltonian parameters between experiments—adds a layer of adaptability critical in real-world contexts where parameters may not remain constant.

Key Results

Through benchmarking on qubit systems, the algorithm proved capable of converging on Hamiltonian parameters efficiently. In single parameter scenarios with known decoherence times, the algorithm demonstrated exponential scaling in precision with experiment count. In two-parameter contexts, where the decoherence time was unknown, the algorithm utilized adaptive controls to effectively learn both the Hamiltonian and noise parameters simultaneously.

The robustness of the algorithm is highlighted by its performance close to the Bayesian Cramer-Rao bound, evidencing near-optimal parameter estimation. Furthermore, the ability to estimate regions—providing credible intervals around learned parameters—offers significant advantages for subsequent quantum control or error correction tasks.

Implications and Future Directions

The practical implications of this research are broad, providing a framework not only for quantum state tomography but also for the characterization needed for quantum error correction in computing devices. This algorithm can significantly aid in the certification of quantum simulations as they reach complexity unmanageable by classical simulations, underpinning future quantum algorithm implementations.

Future developments might include scalability analyses for larger quantum systems with increased parameter dimensions. Additionally, further work on more sophisticated resampling techniques or parallelization strategies can enhance computational efficiency, making the robust online learning of Hamiltonians viable even in expansive quantum architectures.

Overall, the introduction of a tool that is sensitive to changes in experimental parameters and a model’s hyperparameters sets a foundation for more integrated and practically applicable quantum characterization methods applicable across diverse settings in quantum information science.