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Technical Program

Paper Detail

Paper IDD3-S7-T3.3
Paper Title A Theoretical Framework for Learning from Quantum Data
Authors Mohsen Heidari-Khoozani, Purdue University, United States; Arun Padakandla, Wojciech Szpankowski, University of Tennessee, United States
Session D3-S7-T3: Topics in Learning II
Chaired Session: Thursday, 15 July, 00:00 - 00:20
Engagement Session: Thursday, 15 July, 00:20 - 00:40
Abstract Over decades traditional information theory of source and channel coding advances toward learning and effective extraction of information from data. We propose to go one step further and offer a theoretical foundation for learning classical patterns from \textit{quantum data}. However, there are several roadblocks to lay the groundwork for such a generalization. First, classical data must be replaced by a density operator over a Hilbert space. Hence, deviated from problems such as \textit{state tomography}, our samples are i.i.d density operators. The second challenge is even more profound since we must realize that our only interaction with a quantum state is through a measurement which -- due to no-cloning quantum postulate -- loses information after measuring it. With this in mind, we present a quantum counterpart of the well-known PAC framework. Based on that we propose a quantum analogous of the ERM algorithm for learning measurement hypothesis classes. Then, we establish upper bounds on the quantum sample complexity quantum concept classes.