论文标题
某些稀疏矩阵的块编码的显式量子电路
Explicit Quantum Circuits for Block Encodings of Certain Sparse Matrices
论文作者
论文摘要
通过使用最近开发的量子线性代数算法，可以在量子计算机上解决许多标准线性代数问题，该量子算法使用块编码和量子特征值/单数值变换。编码的块嵌入了较大的统一转换U中的适当缩放的矩阵A，该矩阵可以分解为更简单的单位产品，并在量子计算机上有效实现。尽管与最佳的经典算法相比，量子算法可以在解决线性代数问题方面实现指数加速，但效率的增长最终取决于我们构建有效的量子电路的能力，用于a构造A的有效量子电路，这通常是困难的，即使对于良好的稀疏稀疏的稀疏矩阵也不是琐碎的。在本文中，我们提供了一些示例，介绍了如何为一些结构良好的稀疏矩阵明确构建有效的量子电路，并讨论了这些结构中使用的一些策略。我们还提供了MATLAB中这些量子电路的实现。
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding embeds a properly scaled matrix of interest A in a larger unitary transformation U that can be decomposed into a product of simpler unitaries and implemented efficiently on a quantum computer. Although quantum algorithms can potentially achieve exponential speedup in solving linear algebra problems compared to the best classical algorithm, such gain in efficiency ultimately hinges on our ability to construct an efficient quantum circuit for the block encoding of A, which is difficult in general, and not trivial even for well-structured sparse matrices. In this paper, we give a few examples on how efficient quantum circuits can be explicitly constructed for some well-structured sparse matrices, and discuss a few strategies used in these constructions. We also provide implementations of these quantum circuits in MATLAB.
