Online Quantum State Tomography via Stochastic Gradient Descent

• URL: http://arxiv.org/abs/2507.07601v1
• Date: Thu, 10 Jul 2025 10:02:52 GMT
• Title: Online Quantum State Tomography via Stochastic Gradient Descent
• Authors: Jian-Feng Cai, Yuling Jiao, Yinan Li, Xiliang Lu, Jerry Zhijian Yang, Juntao You,
• Abstract summary: We initiate rigorous measurements of online quantum tomography tomography (QST)<n>We show that the algorithms for online low-rank QST both in both in terms of the state rank and the unknown quantum state achieve nearly optimal complexity while with high probability.<n>In particular, our algorithms are better than the state-of-the-art non-efficient Q-of algorithms.
• Score: 15.191189544765427
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We initiate the study of online quantum state tomography (QST), where the matrix representation of an unknown quantum state is reconstructed by sequentially performing a batch of measurements and updating the state estimate using only the measurement statistics from the current round. Motivated by recent advances in non-convex optimization algorithms for solving low-rank QST, we propose non-convex mini-batch stochastic gradient descent (SGD) algorithms to tackle online QST, which leverage the low-rank structure of the unknown quantum state and are well-suited for practical applications. Our main technical contribution is a rigorous convergence analysis of these algorithms. With proper initialization, we demonstrate that the SGD algorithms for online low-rank QST achieve linear convergence both in expectation and with high probability. Our algorithms achieve nearly optimal sample complexity while remaining highly memory-efficient. In particular, their time complexities are better than the state-of-the-art non-convex QST algorithms, in terms of the rank and the logarithm of the dimension of the unknown quantum state.

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