论文标题
量子振幅算术
Quantum Amplitude Arithmetic
论文作者
论文摘要
量子算法涉及对振幅和计算基础的操纵，其中操纵基础在很大程度上是经典计算的量子类似物，这始终是复杂性的主要贡献者。为了充分利用量子机械加速，应在振幅上实现更多的转换。在这里，我们提出了量子振幅算术（QAA）的概念，该概念意图通过在幅度上进行算术操作来发展量子状态。基于乘法和加法操作的基本设计，可以应用QAA来解决黑框量子状态准备问题和量子线性系统问题，并具有相当低的复杂性，并直接评估非线性功能。预计QAA将在各种量子算法中找到应用。
Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor to the complexity. In order to make full use of quantum mechanical speedup, more transformation should be implemented on amplitudes. Here we propose the notion of quantum amplitude arithmetic (QAA) that intent to evolve the quantum state by performing arithmetic operations on amplitude. Based on the basic design of multiplication and addition operations, QAA can be applied to solve the black-box quantum state preparation problem and the quantum linear system problem with fairly low complexity, and evaluate nonlinear functions on amplitudes directly. QAA is expected to find applications in a variety of quantum algorithms.
