Speakers
Description
Quantum computers can solve certain problems out of the reach of their classical counterparts. Among these problems, the (state) hidden subgroup problem -- StateHSP -- has been extensively studied and lies at the core of examples of quantum-classical separations. Solving the StateHSP requires unveiling the structure of a group, and most methods are highly sensitive to noise. In this work, we propose a classical post-processing of samples from a quantum device that enables solutions of the StateHSP on the cyclic groups in the presence of noise. Our method relies on number theory and the strong concentration of the greatest common divisor. Such property allows us to use statistical inference on the output samples and distill signal from noisy backgrounds. Analytical results are given for global and local noise models, as well as numerical explorations of this method for more general noises. Methodologies in this direction might in the future lower the noise-robustness requirements of quantum computers to solve the StateHSP, as well as enhancing the applicability of group theory for imperfectly structured problems.
| Topic | Quantum algorithms for machine learning applications |
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| Additional Topic | Quantum state reconstruction from data |