Neural Network Improves Quantum Tomography

Scientists at Skolkovo Institute of Science and Technology (Skoltech) have applied machine learning to the challenges of reconstructing quantum states. Their findings show that machine learning can reconstruct quantum states from experimental data even in the presence of noise and detection errors.

Members of Skoltech’s Deep Quantum Laboratory collaborated with the quantum optics research laboratories at Moscow State University (MSU) on the research.

The theoretical beam is the goal scientists wished to achieve. Courtesy of “Experimental neural network enhanced quantum tomography,” A. Palmieri et al., https://doi.org/10.1038/s41534-020-0248-6.

To prepare and measure high-dimensional quantum states, the MSU team generated data with an experimental platform based on spatial states of photons. The Skoltech team implemented a deep neural network to analyze the noisy experimental data and learned how to efficiently perform denoising, significantly improving the quality of quantum state reconstruction.

This is a reconstruction with neural networks. Courtesy of “Experimental neural network enhanced quantum tomography,” A. Palmieri et al., https://doi.org/10.1038/s41534-020-0248-6.

To implement their method experimentally, the researchers trained a supervised neural network to filter the experimental data. The neural network uncovered patterns that characterized the measurement probabilities for the original state and the ideal experimental apparatus, free from state-preparation-and-measurement (SPAM) errors.

Experimental data. Courtesy of “Experimental neural network enhanced quantum tomography,” A. Palmieri et al., https://doi.org/10.1038/s41534-020-0248-6.

The researchers compared the neural network state reconstruction protocol with a protocol treating SPAM errors by process tomography and also with a SPAM-agnostic protocol with idealized measurements. The average reconstruction fidelity was shown to be enhanced by 10% and 27%, respectively.

The researchers believe that these results show that the use of a neural network architecture on experimental data could provide a reliable tool for quantum-state-and-detector tomography. The researchers’ approach could apply to the wide range of quantum experiments that rely on tomography.

Quantum tomography is currently used for testing the implementation of quantum information processing devices. Various procedures for state and process reconstruction from measured data have been developed using a model describing state-preparation-and-measurement (SPAM) apparatus.

However, physical models can suffer from intrinsic limitations, as actual measurement operators and trial states cannot be known precisely. This can lead to SPAM errors, degrading reconstruction performance. The researchers’ framework, based on machine learning, can be applied to both the tomography and the mitigation of SPAM errors.

Over the last several years, the researchers have applied a wide range of techniques to reconstructing a quantum state and, surprisingly, have found that deep learning outperformed other methods in experiments.

The research was published in npj Quantum Information (www.doi.org/10.1038/s41534-020-0248-6).