| Paper ID | D3-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.
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