Superfast maximum-likelihood reconstruction for quantum tomography

Jiangwei Shang, Zhengyun Zhang, and Hui Khoon Ng
Phys. Rev. A 95, 062336 – Published 27 June 2017

Abstract

Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we provide a fast and reliable algorithm for maximum-likelihood reconstruction that avoids this slow convergence. Our method utilizes the state-of-the-art convex optimization scheme, an accelerated projected-gradient method, that allows one to accommodate the quantum nature of the problem in a different way than in the standard methods. We demonstrate the power of our approach by comparing its performance with other algorithms for n-qubit state tomography. In particular, an eight-qubit situation that purportedly took weeks of computation time in 2005 can now be completed in under a minute for a single set of data, with far higher accuracy than previously possible. This refutes the common claim that MLE reconstruction is slow and reduces the need for alternative methods that often come with difficult-to-verify assumptions. In fact, recent methods assuming Gaussian statistics or relying on compressed sensing ideas are demonstrably inapplicable for the situation under consideration here. Our algorithm can be applied to general optimization problems over the quantum state space; the philosophy of projected gradients can further be utilized for optimization contexts with general constraints.

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  • Received 20 October 2016
  • Revised 26 May 2017

DOI:https://doi.org/10.1103/PhysRevA.95.062336

©2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Jiangwei Shang1,*, Zhengyun Zhang2,†, and Hui Khoon Ng1,3,4

  • 1Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
  • 2BioSyM IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, Singapore 138602, Singapore
  • 3Yale-NUS College, Singapore 138527, Singapore
  • 4MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654, Singapore

  • *Present address: Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany.
  • zhengyun@smart.mit.edu

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Issue

Vol. 95, Iss. 6 — June 2017

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