arXiv 0809.43172008-09quant-phcs.AR

量子相互作用距离对量子加和电路的影响

On the Effect of Quantum Interaction Distance on Quantum Addition Circuits

Byung-Soo Choi, Rodney Van Meter

备注：: accepted for ACM Journal on Emerging Technologies in Computing Systems
DOI：: 10.1145/2000502.2000504

摘要：

研究了量子相互作用距离对精确量子加法电路速度影响的理论极限。在这项研究中，我们利用图嵌入量子线路分析。我们研究了一个逻辑映射的任何$Ω(\log n)$ -深度量子加法器电路的两个$n$ -量子位寄存器的量子位和门到一个实用的架构，它限制了相互作用的距离，最近的邻居，只支持一个和两个量子位的逻辑门。不幸的是，在所选择的$k$维实际结构上，我们证明了任何精确量子加法电路的深度下界不再是$Ω(\log {n})$，而是$Ω(\sqrt[k]{n})$。这一结果首次将图嵌入应用于量子线路和器件，为编译器开发提供了新的工具，强调了量子计算机体系结构对性能的影响，并在评估量子算法的时间性能时起到警示作用。

英文摘要：

We investigate the theoretical limits of the effect of the quantum interaction distance on the speed of exact quantum addition circuits. For this study, we exploit graph embedding for quantum circuit analysis. We study a logical mapping of qubits and gates of any $Ω(\log n)$-depth quantum adder circuit for two $n$-qubit registers onto a practical architecture, which limits interaction distance to the nearest neighbors only and supports only one- and two-qubit logical gates. Unfortunately, on the chosen $k$-dimensional practical architecture, we prove that the depth lower bound of any exact quantum addition circuits is no longer $Ω(\log {n})$, but $Ω(\sqrt[k]{n})$. This result, the first application of graph embedding to quantum circuits and devices, provides a new tool for compiler development, emphasizes the impact of quantum computer architecture on performance, and acts as a cautionary note when evaluating the time performance of quantum algorithms.

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英文摘要：

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