Quantum Approximation of Normalized Schatten Norms and Applications to Learning
| العنوان: | Quantum Approximation of Normalized Schatten Norms and Applications to Learning |
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| المؤلفون: | Yiyou Chen, Hideyuki Miyahara, Louis-S. Bouchard, Vwani Roychowdhury |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | FOS: Computer and information sciences, Quantum Physics, Computer Science - Machine Learning, FOS: Physical sciences, Quantum Physics (quant-ph), Machine Learning (cs.LG) |
| الوصف: | Efficient measures to determine similarity of quantum states, such as the fidelity metric, have been widely studied. In this paper, we address the problem of defining a similarity measure for quantum operations that can be \textit{efficiently estimated}. Given two quantum operations, $U_1$ and $U_2$, represented in their circuit forms, we first develop a quantum sampling circuit to estimate the normalized Schatten 2-norm of their difference ($\| U_1-U_2 \|_{S_2}$) with precision $\epsilon$, using only one clean qubit and one classical random variable. We prove a Poly$(\frac{1}{\epsilon})$ upper bound on the sample complexity, which is independent of the size of the quantum system. We then show that such a similarity metric is directly related to a functional definition of similarity of unitary operations using the conventional fidelity metric of quantum states ($F$): If $\| U_1-U_2 \|_{S_2}$ is sufficiently small (e.g. $ \leq \frac{\epsilon}{1+\sqrt{2(1/\delta - 1)}}$) then the fidelity of states obtained by processing the same randomly and uniformly picked pure state, $|\psi \rangle$, is as high as needed ($F({U}_1 |\psi \rangle, {U}_2 |\psi \rangle)\geq 1-\epsilon$) with probability exceeding $1-\delta$. We provide example applications of this efficient similarity metric estimation framework to quantum circuit learning tasks, such as finding the square root of a given unitary operation. Comment: 25 pages, 4 figures, 6 tables, 1 algorithm |
| اللغة: | English |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d31735537289e7ad7658e2561b9d9e43 http://arxiv.org/abs/2206.11506 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....d31735537289e7ad7658e2561b9d9e43 |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |