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Efficient estimation and verification of quantum many-body systems

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Q_Estimation.pdf (1.734Mb)
Erstveröffentlichung
2019-10-17
Authors
Holzäpfel, Milan
Referee
Plenio, Martin B.
Ankerhold, Joachim
Dissertation


Faculties
Fakultät für Naturwissenschaften
Institutions
Institut für Theoretische Physik
Institut für Komplexe Quantensysteme
Abstract
Quantum systems and tensors share the property that the complexity of their description grows exponentially with the number of physical subsystems or tensor indices. This thesis discusses efficient methods for tensor reconstruction, quantum state estimation and verification, as well as quantum state and process tomography. The methods proposed here can be efficient in the sense that the resource requirements scale only polynomially instead of exponentially with the number of physical subsystems or tensor indices. In numerical and analytical calculations, matrix product state (MPS)/tensor train (TT), projected entangled pair state (PEPS), and hierarchical Tucker representations are used. The reconstruction and estimation methods are discussed in principle, their performance is evaluated with numerical simulations, and the quantum state in an ion trap quantum simulator experiment is estimated and verified.
Date created
2019
EU Project uulm
BIOQ / Diamond Quantum Devices and Biology / EC / FP7 / 319130
EQUAM / Emulators of Quantum Frustrated Magnetism / EC / FP7 / 323714
QUCHIP / Quantum Simulation on a Photonic Chip / EC / H2020 / 641039
SIQS / Simulators and Interfaces with Quantum Systems / EC / FP7 / 600645
DFG Project THU
JUSTUS / HPC-Cluster Theoretische Chemie / DFG / 236232410
Subject headings
[GND]: Quantenzustand | Spannungstensor | Maximum-Likelihood-Schätzung | Schwellenwert
[LCSH]: Tensor fields | Quantum theory-Mathematics | Mathematical physics
[Free subject headings]: Quantum state estimation | Quantum state tomography | Quantum process tomography | Ancilla-assisted process tomography | Quantum time evolution | Matrix product state | Matrix product operator | Tensor train | Projected entangled pair state | Tucker representation | Tensor reconstruction | Lieb-Robinson bound | Maximum likelihood estimation | Singular value thresholding
[DDC subject group]: DDC 500 / Natural sciences & mathematics | DDC 530 / Physics
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https://oparu.uni-ulm.de/xmlui/license_opod_v1

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DOI & citation

Please use this identifier to cite or link to this item: http://dx.doi.org/10.18725/OPARU-20627

Holzäpfel, Milan (2019): Efficient estimation and verification of quantum many-body systems. Open Access Repositorium der Universität Ulm und Technischen Hochschule Ulm. Dissertation. http://dx.doi.org/10.18725/OPARU-20627
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