Ultrafast quantum state tomography with feed-forward neural networks

Abstract

Reconstructing the state of many-body quantum systems is of fundamental importance in quantum information tasks, but extremely challenging due to the curse of dimensionality. In this work, we present a quantum tomography approach based on neural networks to achieve the ultrafast reconstruction of multi-qubit states. Particularly, we propose a simple 3-layer feed-forward network to process the experimental data generated from measuring each qubit with a positive operator-valued measure, which is able to reduce the storage cost and computational complexity. Moreover, the techniques of state decomposition and $P$-order absolute projection are jointly introduced to ensure the positivity of state matrices learned in the maximum likelihood function and to improve the convergence speed and robustness of the above network. Finally, it is tested on a large number of states with a wide range of purity to show that we can faithfully tomography 11-qubit states on a laptop within 2 minutes under noise. Our numerical results also demonstrate that more state samples are required to achieve the given tomography fidelity for the low-purity states, and the increased depolarizing noise induces a linear decrease in the tomography fidelity