Learning quantum tomography from incomplete measurements

TL;DR

This paper introduces neural network-based methods for quantum state tomography with incomplete measurements, outperforming traditional techniques and enabling more efficient reconstruction by learning optimal measurement sequences.

Contribution

It presents two novel neural network approaches for quantum tomography in incomplete measurement scenarios, including a sequential LSTM method that optimizes measurement sequences.

Findings

Neural network methods outperform maximum likelihood estimation.

The approaches scale to 3- and 4-qubit systems.

Learning measurement sequences improves tomography efficiency.

Abstract

We revisit quantum tomography in an informationally incomplete scenario and propose improved state reconstruction methods using deep neural networks. In the first approach, the trained network predicts an optimal linear or quadratic reconstructor with coefficients depending only on the collection of (already taken) measurement operators. This effectively refines the undercomplete tomographic reconstructor based on pseudoinverse operation. The second, based on an LSTM recurrent network performs state reconstruction sequentially. It can also optimize the measurement sequence, which suggests a no-free-lunch theorem for tomography: by narrowing the state space, we gain the possibility of more efficient tomography by learning the optimal sequence of measurements. Numerical experiments for a 2-qubit system show that both methods outperform standard maximum likelihood estimation and also scale to larger 3- and 4-qubit systems. Our results demonstrate that neural networks can effectively learn the underlying geometry of multi-qubit states using this for their reconstruction.