Learning quantum systems

Abstract

The complexity of quantum systems increases exponentially with their size, but in many practical contexts there are assumptions (such as low rank, sparsity, or a specific type of expected dynamics) that enable classical algorithms to be efficient in the characterization of quantum states, dynamics and measurements. Bayesian inference provides a robust approach to learning models for quantum systems, while preserving physical intuition about the processes involved. Neural networks enable the characterization of complex systems, at the expense of physical intuition. Adaptive approaches, which select the next measurement based on knowledge acquired earlier in the estimation, can speed up the characterization process. Classical optimization and learning algorithms can improve the performance of quantum sensors. The future development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation and sensing. This poses severe challenges in the efficient control, calibration and validation of quantum states and their dynamics. Although the full simulation of large-scale quantum systems may only be possible on a quantum computer, classical characterization and optimization methods still play an important role. Here, we review different approaches that use classical post-processing techniques, possibly combined with adaptive optimization, to learn quantum systems, their correlation properties, dynamics and interaction with the environment. We discuss theoretical proposals and successful implementations across different multiple-qubit architectures such as spin qubits, trapped ions, photonic and atomic systems, and superconducting circuits. This Review provides a brief background of key concepts recurring across many of these approaches with special emphasis on the Bayesian formalism and neural networks. Although the complexity of quantum systems scales exponentially with their size, classical algorithms and optimization strategies can still play an important role in the characterization of quantum states, their dynamics and the detection process.