Reconstructing quantum states with generative models

A major bottleneck in the development of scalable many-body quantum technologies is the difficulty in benchmarking state preparations, which suffer from an exponential 'curse of dimensionality' inherent to the classical description of quantum states. We present an experimentally friendly method for density matrix reconstruction based on neural network generative models. The learning procedure comes with a built-in approximate certificate of the reconstruction and makes no assumptions about the purity of the state under scrutiny. It can efficiently handle a broad class of complex systems including prototypical states in quantum information, as well as ground states of local spin models common to condensed matter physics. The key insight is to reduce state tomography to an unsupervised learning problem of the statistics of an informationally complete quantum measurement. This constitutes a modern machine learning approach to the validation of complex quantum devices, which may in addition prove relevant as a neural-network ansatz over mixed states suitable for variational optimization. Present day quantum technologies enable computations with tens and soon hundreds of qubits. A major outstanding challenge is to measure and benchmark the complete quantum state, a task that grows exponentially with the system size. Generative models based on restricted Boltzmann machines and recurrent neural networks can be employed to solve this quantum tomography problem in a scalable manner.