Neural-shadow quantum state tomography: applications for near-term quantum devices*

Neural network quantum state is a classical ansatz that has been implemented successfully in reconstructing quantum states from measurement data. In this process, known as neural network quantum state tomography (NNQST), a neural network is trained using a cross-entropy loss function to get the amplitudes and relative phases of a pure quantum state. However, NNQST often has difficulty in determining the relative phases of a quantum state. In this talk, we propose an alternative neural network-based protocol, which we call neural-shadow quantum state tomography (NSQST). NSQST uses infidelity as a loss function and combines classical shadows with computational basis measurements via a pretraining procedure. Here, the infidelity loss function is efficiently estimated using classical shadows of the target state. We demonstrate that NSQST has an advantage over NNQST in learning the relative phases of target quantum states and offers noise robustness in the case of Clifford shadows. We further focus on the implementation and usefulness of this protocol in near-term quantum devices.