论文标题
Harrow-Hassidim-lloyd算法的数字分析共同设计
Digital-analog co-design of the Harrow-Hassidim-Lloyd algorithm
论文作者
论文摘要
提出了Harrow-Hassidim-lloyd量子算法来求解方程的线性系统$ a \ vec {x} = \ vec {b} $，它是各种应用程序的核心。但是，子例程没有明确的量子电路，它将问题矩阵$ a $的倒数映射到辅助量子位中。这使得在当前的量子设备中挑战实施，迫使我们使用混合方法。在这里，我们提出了一种系统的方式来实现此子例程，该子例程可以适应矩阵$ a $的其他功能$ f（a）$，我们提出了一个共同设计的量子处理器，以减少算法的深度，我们介绍了其数字 - Analog实施。我们的提案的深度以精度$ε$为$ \ MATHCAL {o}（ε^{ - 1}）$缩放，该$受某个实验允许的样本数量的界限。 Harrow-Hassidim-lloyd算法的共同设计导致“风筝样”架构，这使我们能够减少所需的交换门的数量。最后，将共同设计的量子处理器结构与数字分析实现合并有助于在算法实现过程中降低噪声源。
The Harrow-Hassidim-Lloyd quantum algorithm was proposed to solve linear systems of equations $A\vec{x} = \vec{b}$ and it is the core of various applications. However, there is not an explicit quantum circuit for the subroutine which maps the inverse of the problem matrix $A$ into an ancillary qubit. This makes challenging the implementation in current quantum devices, forcing us to use hybrid approaches. Here, we propose a systematic manner to implement this subroutine, which can be adapted to other functions $f(A)$ of the matrix $A$, we present a co-designed quantum processor which reduces the depth of the algorithm, and we introduce its digital-analog implementation. The depth of our proposal scales with the precision $ε$ as $\mathcal{O}(ε^{-1})$, which is bounded by the number of samples allowed for a certain experiment. The co-design of the Harrow-Hassidim-Lloyd algorithm leads to a "kite-like" architecture, which allows us to reduce the number of required SWAP gates. Finally, merging a co-design quantum processor architecture with a digital-analog implementation contributes to the reduction of noise sources during the experimental realization of the algorithm.
