Quantum Approximation of Normalized Schatten Norms and Applications to Learning. (arXiv:2206.11506v1 [quant-ph])

Web: http://arxiv.org/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
\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 …

applications approximation arxiv learning quantum