Abstract
Online quantum state learning is a recently proposed problem by Aaronson et al. (2018), where the learner sequentially predicts $n$-qubit quantum states based on given measurements on states and noisy outcomes. In the previous work, the algorithms are worst-case optimal in general but fail in achieving tighter bounds in certain simpler or more practical cases. In this paper, we develop algorithms to advance the online learning of quantum states. First, we show that Regularized Follow-the-Leader (RFTL) method with Tallis-2 entropy can achieve an $O(sqrtMT)$ total loss with perfect hindsight on the first $T$ measurements with maximum rank $M$. This regret bound depends only on the maximum rank $M$ of measurements rather than the number of qubits, which takes advantage of low-rank measurements. Second, we propose a parameter-free algorithm based on a classical adjusting learning rate schedule that can achieve a regret depending on the loss of best states in hindsight, which takes advantage of low noisy outcomes. Besides these more adaptive bounds, we also show that our RFTL with Tallis-2 entropy algorithm can be implemented efficiently on near-term quantum computing devices, which is not achievable in previous works.
Xin Wang
Associate Professor
Prof. Xin Wang founded the QuAIR lab at HKUST(Guangzhou) in June 2023. His research primarily focuses on better understanding the limits of information processing with quantum systems and the power of quantum artificial intelligence. Prior to establishing the QuAIR lab, Prof. Wang was a Staff Researcher at the Institute for Quantum Computing at Baidu Research, where he concentrated on quantum computing research and the development of the Baidu Quantum Platform. Notably, he spearheaded the development of Paddle Quantum, a Python library designed for quantum machine learning. From 2018 to 2019, Prof. Wang held the position of Hartree Postdoctoral Fellow at the Joint Center for Quantum Information and Computer Science (QuICS) at the University of Maryland, College Park. He earned his doctorate in quantum information from the University of Technology Sydney in 2018, under the guidance of Prof. Runyao Duan and Prof. Andreas Winter. In 2014, Prof. Wang obtained his B.S. in mathematics (with Wu Yuzhang Honor) from Sichuan University.