# Experimental neural network enhanced quantum tomography

## TL;DR

This paper introduces a machine learning protocol using neural networks to reduce SPAM errors in quantum tomography, significantly improving state reconstruction fidelity in quantum experiments.

## Contribution

The paper develops and experimentally demonstrates a neural network-based method to mitigate SPAM errors in quantum state tomography, enhancing accuracy over existing protocols.

## Key findings

- Neural network filtering improves reconstruction fidelity by 10%.
- The method achieves a 27% fidelity increase compared to SPAM-agnostic protocols.
- Experimental validation confirms effectiveness across quantum tomography scenarios.

## Abstract

Quantum tomography is currently ubiquitous for testing any implementation of a quantum information processing device. Various sophisticated procedures for state and process reconstruction from measured data are well developed and benefit from precise knowledge of the model describing state preparation and the measurement apparatus. However, physical models suffer from intrinsic limitations as actual measurement operators and trial states cannot be known precisely. This scenario inevitably leads to state-preparation-and-measurement (SPAM) errors degrading reconstruction performance. Here we develop and experimentally implement a machine learning based protocol reducing SPAM errors. We trained a supervised neural network to filter the experimental data and hence uncovered salient patterns that characterize the measurement probabilities for the original state and the ideal experimental apparatus free from SPAM errors. We compared the neural network state reconstruction protocol with a protocol treating SPAM errors by process tomography, as well as to a SPAM-agnostic protocol with idealized measurements. The average reconstruction fidelity is shown to be enhanced by 10\% and 27\%, respectively. The presented methods apply to the vast range of quantum experiments which rely on tomography.