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Physical Review Applied

Quantum process overlapping tomography: Theory and experiment

Yi Hu, Congcong Zheng, Xiaojun Wang, Zaichen Zhang, Ping Xu, Kun Wang

Published May 29, 2025• 0 citations
Publisher
DOI
10.1103/jkf7-wfcn

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Quantum information science and technology is experiencing rapid development. The process raises an emerging demand for experiments to implement and demonstrate novel ideas to overcome the challenges towards the further application of quantum information. Linear optical systems have long been the most available and efficient platform for the demonstration of quantum information methods and concepts due to its robustness against the influence of environment. However, the large-scale multi-qubit linear optical information systems have long been suffering the low generated efficiency of the single photon sources, leading to a limited availability and scalability. In recent years, novel techniques such as beam-like SPDC open up new possibilities to break this bottleneck and further develop linear optical quantum information systems. Driven by the increasing demand and inspired by the technical progress, in my degree candidature, I carried out a project to build an advanced linear optical multi-qubit experimental platform to implement quantum information experiment and to discover novel methodologies of quantum optics research. In this thesis, I will present our progress and future perspectives. In Chapters 1-2, I will introduce the background and the motivation of this project first, and then present the basic concepts and principles of linear optical quantum information that are involved in my research. Chapter 3 describes my work on the generation and measurement of linear optical multi-qubit entanglement based on beam-like SPDC sources. By analyzing and containing the entanglement destruction from time-space correlation and group delay dispersion, the specifications of linear optical multi-qubit system can reach a higher level that allows for more applications. In Chapter 4, we discuss the methodology we developed to statistically estimate quantum states based on measurement results. In this project, we developed and applied a new algorithm named Bayesian mean estimation based on Gibbs sampling to estimate quantum states. I will describe the background, principle, and advantages compared to other widely accepted methods of this algorithm. In Chapter 5, I report our progress in experimentally demonstrating quantum overlapping tomography, a scheme focusing on characterizing critical information of a many-body quantum system in logarithmic time complexity. We compare the estimate results of full-state tomography and overlapping tomography to confirm that overlapping tomography gives accurate information of the system with much fewer state measurements than full-state tomography. Furthermore, under the condition that the system is too large to perform a tomography, we confirm that the state is still able to be measured with overlapping tomography. Chapter 6 begins with the conclusion of the thesis. Furthermore, I present outlooks on some potential directions to further increase the linear optical quantum information system.

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Quantum overlapping tomography (QOT), which focuses on reconstructing subsystems of quantum systems, has emerged as a promising approach for quantum state learning, especially when full-state tomography is infeasible. QOT has attracted considerable interest and seen substantial development, but has not yet reached its ultimate limit. The authors introduce a unified framework for optimal QOT by mapping the problem to the ``clique cover'' model from graph theory. This framework provides superlative efficiency and experimental feasibility in measurement strategies. This validation of QOT's utility paves the way for advanced quantum system characterization and state-property learning.
Characterizing large-scale quantum systems is central to fundamental physics and essential for applications of quantum technologies. While a full characterization requires exponentially increasing resources, focusing on application-relevant information can often lead to significantly simplified analysis. Overlapping tomography is such a scheme, allowing one to obtain all the information contained in specific subsystems of multiparticle quantum systems in an efficient manner, but the ultimate limits of this approach remain elusive. We present protocols for overlapping tomography that are optimal with respect to the number of measurement settings. First, by providing algorithmic approaches based on graph theory we find the minimal number of Pauli settings, relating overlapping tomography to the problem of covering arrays in combinatorics. This significantly reduces the number of measurement settings, showing for instance that two-body overlapping tomography of nearest neighbors in qubit systems with planar topologies can always be performed with nine Pauli settings. Second, we prove that using general projective measurements, all k-body marginals can be reconstructed with only 3^{k} settings, 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 characterizing fermionic systems in quantum chemistry.
Quantum information science and technology is experiencing rapid development. The process raises an emerging demand for experiments to implement and demonstrate novel ideas to overcome the challenges towards the further application of quantum information. Linear optical systems have long been the most available and efficient platform for the demonstration of quantum information methods and concepts due to its robustness against the influence of environment. However, the large-scale multi-qubit linear optical information systems have long been suffering the low generated efficiency of the single photon sources, leading to a limited availability and scalability. In recent years, novel techniques such as beam-like SPDC open up new possibilities to break this bottleneck and further develop linear optical quantum information systems. Driven by the increasing demand and inspired by the technical progress, in my degree candidature, I carried out a project to build an advanced linear optical multi-qubit experimental platform to implement quantum information experiment and to discover novel methodologies of quantum optics research. In this thesis, I will present our progress and future perspectives. In Chapters 1-2, I will introduce the background and the motivation of this project first, and then present the basic concepts and principles of linear optical quantum information that are involved in my research. Chapter 3 describes my work on the generation and measurement of linear optical multi-qubit entanglement based on beam-like SPDC sources. By analyzing and containing the entanglement destruction from time-space correlation and group delay dispersion, the specifications of linear optical multi-qubit system can reach a higher level that allows for more applications. In Chapter 4, we discuss the methodology we developed to statistically estimate quantum states based on measurement results. In this project, we developed and applied a new algorithm named Bayesian mean estimation based on Gibbs sampling to estimate quantum states. I will describe the background, principle, and advantages compared to other widely accepted methods of this algorithm. In Chapter 5, I report our progress in experimentally demonstrating quantum overlapping tomography, a scheme focusing on characterizing critical information of a many-body quantum system in logarithmic time complexity. We compare the estimate results of full-state tomography and overlapping tomography to confirm that overlapping tomography gives accurate information of the system with much fewer state measurements than full-state tomography. Furthermore, under the condition that the system is too large to perform a tomography, we confirm that the state is still able to be measured with overlapping tomography. Chapter 6 begins with the conclusion of the thesis. Furthermore, I present outlooks on some potential directions to further increase the linear optical quantum information system.