标题： 变分量子奇异值分解中的矩阵编码方法 显示英文标题

标题： Matrix encoding method in variational quantum singular value decomposition

摘要： 我们提出了一种基于将所考虑的{ $N\times N$}矩阵的元素编码到适当维度的量子系统状态中的变分量子奇异值分解方法。 此方法不使用该矩阵在单位矩阵展开中的表示。 涉及受控测量以避免辅助量子比特测量中的小成功概率。 可以通过对{二}个单量子比特子系统的状态进行测量，概率性地获得最大化算法的目标函数。 该电路需要$O(\log N)$个量子比特来实现该算法，其深度与$ \log N/\varepsilon$成比例，其中$\varepsilon$是计算奇异值所需的精度。 显示英文摘要

摘要： We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of this matrix in terms of the unitary matrices. Controlled measurement is involved to avoid small success probability in ancilla measurement. The objective function for maximization algorithm can be obtained probabilistically via measurement of the states of { two} one-qubit subsystems. The circuit requires $O(\log N)$ qubits for realization of this algorithm { whose depths is proportional to $ \log N/\varepsilon$, where $\varepsilon$ is the precision required for calculation of singular values.