Optimal overlapping tomography

• URL: http://arxiv.org/abs/2408.05730v1
• Date: Sun, 11 Aug 2024 08:59:08 GMT
• Title: Optimal overlapping tomography
• Authors: Kiara Hansenne, Rui Qu, Lisa T. Weinbrenner, Carlos de Gois, Haifei Wang, Yang Ming, Zhengning Yang, Paweł Horodecki, Weibo Gao, Otfried Gühne,
• Abstract summary: Overlapping tomography is a scheme which allows to obtain all the information contained in specific subsystems of quantum systems. We present protocols for optimal overlapping tomography with respect to different figures of merit. Results will find applications in learning noise and interaction patterns in quantum computers as well as characterising fermionic systems in quantum chemistry.
• Score: 0.814548016007804
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Characterising large scale quantum systems is central for fundamental physics as well as for applications of quantum technologies. While a full characterisation requires exponentially increasing effort, focusing on application-relevant information can often lead to significantly simplified analysis. Overlapping tomography is such a scheme, which allows to obtain all the information contained in specific subsystems of multi-particle quantum systems in an efficient manner, but the ultimate limits of this approach remained elusive. We present protocols for optimal overlapping tomography with respect to different figures of merit. First, by providing algorithmic approaches based on graph theory we find the optimal scheme for Pauli measurements on qubits, relating it to the problem of covering arrays in combinatorics. This significantly reduces the measurement effort, showing for instance that two-body overlapping tomography of nearest neighbours in multiqubit quantum systems can always be performed with nine Pauli settings. Second, we prove that the optimal scheme using general projective measurements requires only $3^k$ settings to reconstruct all $k$-body marginals, independently of the system size. Finally, we demonstrate the practical applicability of our methods in a six-photon experiment. Our results will find applications in learning noise and interaction patterns in quantum computers as well as characterising fermionic systems in quantum chemistry.

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