Quantum algorithms for approximate function loading

Loading classical data into quantum computers represents an essential stage in many relevant algorithms, especially the field of machine learning. Therefore, inefficiency this loading process means a major bottleneck for application these algorithms. Here, we introduce two approximate quantum-state preparation methods noisy intermediate-scale era inspired by Grover-Rudolph algorithm, which partially solve problem real functions. Indeed, allowing infidelity $\ensuremath{\epsilon}$ and under certain smoothness conditions, prove that complexity implementation algorithm without ancillary qubits, first introduced M\"ott\"onen et al., results $\mathcal{O}({2}^{{k}_{0}(\ensuremath{\epsilon})})$, with $n$ number qubits ${k}_{0}(\ensuremath{\epsilon})$ asymptotically independent $n$. This leads to dramatic reduction required two-qubit gates. Aroused result, also propose variational capable functions beyond aforementioned conditions. Our Ansatz is explicitly tailored landscape function, leading quasioptimized hyperparameters. allows us achieve high fidelity loaded state speed convergence studied examples.