Neural-network-assisted quantum state and process tomography using limited data sets

In this study we employ a feed-forward artificial neural network (FFNN) architecture to perform the tomography of quantum states and processes obtained from noisy experimental data. To evaluate the performance of the FFNN, we use a heavily reduced data set and show that the density and process matrices of unknown quantum states and processes can be reconstructed with high fidelity. We use the FFNN model to tomograph 100 two-qubit and 128 three-qubit states which were experimentally generated on a nuclear magnetic resonance (NMR) quantum processor. The FFNN model is further used to characterize different quantum processes including two-qubit entangling gates, a shaped pulsed field gradient, intrinsic decoherence processes present in an NMR system, and various two-qubit noise channels (correlated bit flip, correlated phase flip, and a combined bit and phase flip). The results obtained via the FFNN model are compared with standard quantum state and process tomography methods and the computed fidelities demonstrates that, for all cases, the FFNN model outperforms the standard methods for tomography.