https://doi.org/10.1140/epjqt/s40507-023-00181-2
Research
Optimal quantum state tomography with noisy gates
1
Department of Physics, University of Konstanz, D-78457, Konstanz, Germany
2
Zukunftskolleg, University of Konstanz, D-78457, Konstanz, Germany
3
Department of Mathematical Foundations of Computer Sciences, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Akad. G. Bonchev, block 8, 1113, Sofia, Bulgaria
a
violeta.ivanova-rohling@uni-konstanz.de
Received:
7
March
2023
Accepted:
14
June
2023
Published online:
28
June
2023
Quantum state tomography (QST) represents an essential tool for the characterization, verification, and validation (QCVV) of quantum processors. Only for a few idealized scenarios, there are analytic results for the optimal measurement set for QST. E.g., in a setting of non-degenerate measurements, an optimal minimal set of measurement operators for QST has eigenbases which are mutually unbiased. However, in other set-ups, dependent on the rank of the projection operators and the size of the quantum system, the optimal choice of measurements for efficient QST needs to be numerically approximated. We have generalized this problem by introducing the framework of customized efficient QST. Here we extend customized QST and look for the optimal measurement set for QST in the case where some of the quantum gates applied in the measurement process are noisy. To achieve this, we use two distinct noise models: first, the depolarizing channel, and second, over- and under-rotation in single-qubit and to two-qubit gates (for further information, please see Methods). We demonstrate the benefit of using entangling gates for the efficient QST measurement schemes for two qubits at realistic noise levels, by comparing the fidelity of reconstruction of our optimized QST measurement set to the state-of-the-art scheme using only product bases.
Key words: Quantum tomography / High-dimensional optimization problem / Quantum gates / Noise / Quantum computing
Violeta N. Ivanova-Rohling and Niklas Rohling contributed equally to this work.
© The Author(s) 2023
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
