Quantum State Tomography: Neural Network Approach

This lecture introduces a novel approach to quantum state tomography using a differential neural network based on the restricted Boltzmann machine (RBM). The RBM architecture, with visible and hidden layers, is explained in detail, emphasizing its energy-based model similar to physics principles. The lecture covers the training process for amplitude and phase parameters separately, utilizing gradients and KL divergence. Results are presented for various scenarios, including the W state and 1D lattice systems, showcasing the RBM's accuracy in predicting quantum states. The importance of measuring amplitude and phase in quantum tomography is highlighted, along with the challenges of decoupling them. The lecture concludes by discussing the potential applications of this approach beyond RBMs, such as feedforward networks.