aiqbench analysis
This research establishes a unified mathematical framework that enables quantum tomography protocols to achieve optimal accuracy scaling proportional to $O(1/N)$, surpassing the standard $O(1/\sqrt{N})$ limit of static methods. By introducing adaptive algorithms validated through both simulations and optical experiments, the study provides a rigorous path toward more efficient characterization of quantum states, detectors, and processes. These advances are critical for scaling up quantum hardware verification without exponentially increasing resource consumption.
Unified formalism and adaptive algorithms for optimal quantum state, detector and process tomography
arXiv:2509.05988v2 Announce Type: replace Abstract: Quantum tomography is a standard technique for characterizing, benchmarking and verifying quantum systems/devices and plays a vital role in advancing quantum technology and understanding the foundations of quantum mechanics. Achieving the highest possible tomography accuracy remains a central challenge. Here we unify the infidelity metrics for quantum state, detector and process tomography in a single index $1-F(\hat S,S)$, where $S$ represents the true density matrix, POVM element, or process matrix, and $\hat S$ is its estimator. We establish a sufficient and necessary condition for any tomography protocol to attain the optimal scaling $1-F= O(1/N) $ where $N$ is the number of state copies consumed, in contrast to the $O(1/\sqrt{N})$ worst-case scaling of static methods. Guided by this result, we propose adaptive algorithms with provably optimal infidelity scalings for state, detector, and process tomography. Numerical simulations and quantum optical experiments validate the proposed methods, with our experiments reaching, for the first time, the optimal infidelity scaling in ancilla-assisted process tomography.
Authors:Shuixin Xiao, Xiangyu Wang, Yuanlong Wang, Zhibo Hou, Jun Zhang, Ian R. Petersen, Wen-Zhe Yan, Hidehiro Yonezawa, Franco Nori, Guo-Yong Xiang, Daoyi Dong
Abstract:Quantum tomography is a standard technique for characterizing, benchmarking and verifying quantum systems/devices and plays a vital role in advancing quantum technology and understanding the foundations of quantum mechanics. Achieving the highest possible tomography accuracy remains a central challenge. Here we unify the infidelity metrics for quantum state, detector and process tomography in a single index $1-F(\hat S,S)$, where $S$ represents the true density matrix, POVM element, or process matrix, and $\hat S$ is its estimator. We establish a sufficient and necessary condition for any tomography protocol to attain the optimal scaling $1-F= O(1/N) $ where $N$ is the number of state copies consumed, in contrast to the $O(1/\sqrt{N})$ worst-case scaling of static methods. Guided by this result, we propose adaptive algorithms with provably optimal infidelity scalings for state, detector, and process tomography. Numerical simulations and quantum optical experiments validate the proposed methods, with our experiments reaching, for the first time, the optimal infidelity scaling in ancilla-assisted process tomography.
arXiv:2509.05988 [quant-ph]
(or arXiv:2509.05988v2 [quant-ph] for this version)
Full text under the publisher's open licence · 190 words
