A moment-based variational approach to tomographic reconstruction

Caption title.Includes bibliographical references (p. 24-26).Supported by the National Science Foundation. 9015281-MIP Supported by the Office of Naval Research. N00014-91-J-1004 Supported by the US Army Research Office. DAAL03-92-G-0115 Supported by the Clement Vaturi Fellowship in Biomedical Imaging Sciences at MIT.Peyman Milanfar, W. Clem Karl, Alan S. Willsky

Continuous matrix product state tomography of quantum transport experiments

In recent years, a close connection between the description of open quantum systems, the input-output formalism of quantum optics, and continuous matrix product states in quantum field theory has been established. So far, however, this connection has not been extended to the condensed-matter context. In this work, we substantially develop further and apply a machinery of continuous matrix product states (cMPS) to perform tomography of transport experiments. We first present an extension of the tomographic possibilities of cMPS by showing that reconstruction schemes do not need to be based on low-order correlation functions only, but also on low-order counting probabilities. We show that fermionic quantum transport settings can be formulated within the cMPS framework. This allows us to present a reconstruction scheme based on the measurement of low-order correlation functions that provides access to quantities that are not directly measurable with present technology. Emblematic examples are high-order correlations functions and waiting times distributions (WTD). The latter are of particular interest since they offer insights into short-time scale physics. We demonstrate the functioning of the method with actual data, opening up the way to accessing WTD within the quantum regime.Comment: 11 pages, 4 figure

Tomographic Reconstruction from a Few Views: A Multi-Marginal Optimal Transport Approach

19 pagesInternational audienceIn this article, we focus on tomographic reconstruction. The problem is to determine the shape of the interior interface using a tomographic approach while very few X-ray radiographs are performed. We use a multi-marginal optimal transport approach. Preliminary numerical results are presented

A variational method for tomographic reconstruction with few views

In this article, we focus on tomographic reconstruction. The problem is to determine the shape of the interior interface using a tomographic approach while very few X-ray radiographs are performed. We present a variational model and numerical analysis. We use a modified Nesterov algorithm to compute the solution. Numerical results are presented

Quantum field tomography

We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product states, a complete set of variational states grasping states in quantum field theory. We innovate a practical method, making use of and developing tools in estimation theory used in the context of compressed sensing such as Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum field states based on low-order correlation functions. In the absence of a phase reference, we highlight how specific higher order correlation functions can still be predicted. We exemplify the functioning of the approach by reconstructing randomised continuous matrix product states from their correlation data and study the robustness of the reconstruction for different noise models. We also apply the method to data generated by simulations based on continuous matrix product states and using the time-dependent variational principle. The presented approach is expected to open up a new window into experimentally studying continuous quantum systems, such as encountered in experiments with ultra-cold atoms on top of atom chips. By virtue of the analogy with the input-output formalism in quantum optics, it also allows for studying open quantum systems.Comment: 31 pages, 5 figures, minor change