Quantum state tomography of multi-qubit systems—a comparative study

Multi-qubit state tomography is a key problem in quantum information technology, which has been studied extensively. In this work, we focus on multi-qubit state tomography based on neural network estimators and typical conventional estimation approaches. For multi-qubit pure states, fully connected neural networks and restricted Boltzmann machine networks are designed, respectively, to carry out state tomography of 2-qubit (low-dimensional) systems and 5-qubit (high-dimensional) systems. Comparisons are made with maximum likelihood estimation and least squares estimation, where performance indicators are selected as reconstruction accuracy, time cost and the number of parameters. Simulation results indicate that intelligent approaches have significant advantages over conventional approaches for state tomography of low-dimensional systems; for high-dimensional systems, however, the conventional approach is still dominant when the measurement is complete, while the restricted Boltzmann machine network can achieve higher reconstruction accuracy when the measurement is incomplete.