论文标题
没有Ancilla seleclection的Harrow-Hassidim-lloyd算法
Harrow-Hassidim-Lloyd algorithm without ancilla postselection
论文作者
论文摘要
Harrow-Hassidim-lloyd算法（HHL）允许实现线性方程系统的指数更快解决方案。但是，该算法要求安排量子置位后获得解决方案。此序列使算法结果概率。在这里，我们显示了当HHL算法可以在不选择Ancilla Qubit的情况下工作时的条件。当用$ \ ket {0} $和$ \ ket {1} $测量Ancilla Qubit时，我们得出了HHL结果状态下可观察到的$ m $的期望值，并显示了无邮政为选择的HHL运行条件。我们提供了一个实践间隔的输入矩阵和可观察的可观察的示例，该矩阵满足了无选择的HHL条件。我们的工作可以提高基于HHL的算法的性能。
Harrow-Hassidim-Lloyd algorithm (HHL) allows for the exponentially faster solution of a system of linear equations. However, this algorithm requires the postselection of an ancilla qubit to obtain the solution. This postselection makes the algorithm result probabilistic. Here we show conditions when the HHL algorithm can work without postselection of ancilla qubit. We derive expectation values for an observable $M$ on the HHL outcome state when ancilla qubit is measured in $\ket{0}$ and $\ket{1}$ and show condition for postselection-free HHL running. We provide an explicit example of a practically-interesting input matrix and an observable, which satisfy postselection-free HHL condition. Our work can improve the performance of the HHL-based algorithms.
