改进了反射操作符的实现
Improved implementation of reflection operators
摘要：
用于不同问题（包括搜索和优化问题）的量子算法需要在目标状态上实现反射算子。通常，使用相位估计来近似地实现这样的反射。在这里，我们使用幺正的线性组合和振幅放大的版本来近似反射算子的幺正算子的本征向量使用指数较少的辅助量子比特的精度参数。我们的方法的门的复杂度也是相估计的方法在一定的限制的兴趣。像相位估计一样，我们的方法需要执行受控的酉运算。然后，我们将我们的结果扩展到哈密顿的情况下，目标状态是一个特征向量的哈密顿矩阵元素可以查询。我们的结果是有用的，因为它们减少了文献中各种量子算法所需的资源。我们的改进还依赖于一个有效的量子算法来准备一个具有类似高斯振幅的量子态，这可能是独立的兴趣。我们还提供了在量子计算机上实现近似反射算子的查询复杂度的下限。
英文摘要：
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation. Here we use a linear combination of unitaries and a version of amplitude amplification to approximate reflection operators over eigenvectors of unitary operators using exponentially less ancillary qubits in terms of a precision parameter. The gate complexity of our method is also comparable to that of the phase estimation approach in a certain limit of interest. Like phase estimation, our method requires the implementation of controlled unitary operations. We then extend our results to the Hamiltonian case where the target state is an eigenvector of a Hamiltonian whose matrix elements can be queried. Our results are useful in that they reduce the resources required by various quantum algorithms in the literature. Our improvements also rely on an efficient quantum algorithm to prepare a quantum state with Gaussian-like amplitudes that may be of independent interest. We also provide a lower bound on the query complexity of implementing approximate reflection operators on a quantum computer.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
