# Quantum Approximation of Normalized Schatten Norms and Applications to Learning

@article{Chen2022QuantumAO, title={Quantum Approximation of Normalized Schatten Norms and Applications to Learning}, author={Yiyou Chen and Hideyuki Miyahara and Louis-S. Bouchard and Vwani P. Roychowdhury}, journal={ArXiv}, year={2022}, volume={abs/2206.11506} }

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 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 ( (cid:107) U 1 − U 2 (cid:107) S 2 ) with precision (cid:15) , using…

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