Experimental neural network enhanced quantum tomography

Adriano Macarone Palmieri,Dmitry Yudin,Sergei Kulik,Federico Bianchi,Stanislav Straupe,Egor Kovlakov,Jacob D Biamonte

doi:10.1038/s41534-020-0248-6

Adriano Macarone Palmieri, Dmitry Yudin + Show 5 more

Open Access

https://doi.org/10.1038/s41534-020-0248-6

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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-measurement (SPAM) apparatus. However, physical models suffer from intrinsic limitations as actual measurement operators and trial states cannot be known precisely. This scenario inevitably leads to SPAM errors degrading reconstruction performance. Here we develop a framework based on machine learning which generally applies to both the tomography and SPAM mitigation problem. We experimentally implement our method. 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 an 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.

Highlights

Rapid experimental progress realizing quantum enhanced technologies places an increased demand on methods for validation and testing
Our method compensates for measurement errors of the specific experimental apparatus employed, as we demonstrate on real experimental data from high-dimensional quantum states of single photons encoded in spatial modes
Our results were obtained with analytical correction for some known SPAM errors already performed

Summary

INTRODUCTION

Rapid experimental progress realizing quantum enhanced technologies places an increased demand on methods for validation and testing. The reconstruction procedure requires knowledge of the measurement operators {Mαγ}, as well as the test states {ρα} in the case of process tomography Both tend to deviate from the experimenter’s expectations due to stochastic noise and systematic errors. The most straightforward approach is calibration of the measurement setup with some close-to-ideal and easy to prepare test states, or calibration of the preparation setup with known and close-to-ideal measurements In this case, one may infer the processes R and/or M explicitly—for example—in the form of the corresponding operator elements, and incorporate this knowledge in the reconstruction procedure. We assume, that all the SPAM errors can be attributed to the measurement part of the setup, and the state preparation may be performed reliably This is the case in our experimental implementation (see Supplementary Material).

DISCUSSION

Findings

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