Quantum State Tomography with Mode-assisted Training

As a tool to model many-body systems, restricted Boltzmann machines (RBMs) have achieved some success when applied to the task of quantum state tomography. However, RBMs are notoriously hard to train, as the computation of the exact gradient is intractable, and estimation with Gibbs sampling is expensive and inefficient. Here, we show that, with the introduction of an off-gradient training step constructed from the mode of the RBM distribution (which we call ``mode-assisted training"), we can improve the quality of quantum state tomography significantly, while reducing the number of required measurements. We employ a novel computing paradigm, MemComputing, to sample the mode efficiently.