دسته بندی:
محاسبات کوانتومی - Quantum-Computing
سال انتشار:
2022
عنوان انگلیسی مقاله:
A Low-Complexity Quantum Principal Component Analysis Algorithm
ترجمه فارسی عنوان مقاله:
یک الگوریتم تحلیل مولفه اصلی کوانتومی با پیچیدگی کم
منبع:
ieee - ieee Transactions on Quantum Engineering;2022;3; ;10:1109/TQE:2021:3140152
نویسنده:
CHEN HE (Member, IEEE), JIAZHEN LI, WEIQI LIU , JINYE PENG, AND Z. JANE WANG
چکیده انگلیسی:
In this article, we propose a low-complexity quantum principal component analysis (qPCA)
algorithm. Similar to the state-of-the-art qPCA, it achieves dimension reduction by extracting principal
components of the data matrix, rather than all components of the data matrix, to quantum registers, so that the
samples of measurement required can be reduced considerably. Both our qPCA and Lin’s qPCA are based
on quantum singular-value thresholding (QSVT). The key of Lin’s qPCA is to combine QSVT, and modified
QSVT is to obtain the superposition of the principal components. The key of our algorithm, however, is to
modify QSVT by replacing the rotation-controlled operation of QSVT with the controlled-not operation
to obtain the superposition of the principal components. As a result, this small trick makes the circuit
much simpler. Particularly, the proposed qPCA requires three phase estimations, while the state-of-the-art
qPCA requires five phase estimations. Since the runtime of qPCA mainly comes from phase estimations, the
proposed qPCA achieves a runtime of roughly 3/5 of that of the state of the art. We simulate the proposed
qPCA on the IBM quantum computing platform, and the simulation result verifies that the proposed qPCA
yields the expected quantum state.
INDEX TERMS: Quantum computing | quantum principal component analysis (qPCA) | quantum singular value threshold.
قیمت: رایگان
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