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Frontiers in Optics

Efficient Algorithms for Quantum State and Process Tomography

Andrew C. Doherty

Published Jan 1, 2009• 1 citation
Publisher

Abstract

This talk will introduce numerical and analytical techniques of convex optimization. While these techniques have found wide application in quantum information, we will focus on applications to data analysis in quantum state and process tomography.
DOI
10.1364/fio.2009.jtub1

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Quantum state tomography (QST) is a technique for characterizing, benchmarking, and verifying quantum systems and devices. In this paper, we focus on collective QST using data from collective measurements performed on multiple copies of the state. We propose a closed-form solution and provide an analytical characterization of its computational complexity and mean squared error (MSE) scaling. Additionally, we reformulate the problem as a sum of squares (SOS) optimization problem with semialgebraic constraints, enabling the application of SOS tools for its solution. The effectiveness of the proposed methods is demonstrated through numerical simulations. Furthermore, we validate the algorithms using two-copy collective experimental data, where the entangled measurement provides information about the state purity. Compared to previous methods, our algorithms achieve lower MSEs and approach the collective MSE bound by leveraging this purity information more efficiently.