计算二维目标电磁散射截面的量子线性系统算法的具体资源分析
Concrete resource analysis of the quantum linear system algorithm used to compute the electromagnetic scattering cross section of a 2D target
摘要：
我们提供了一个详细的估计量子线性系统算法（QLSA）的逻辑资源需求[物理。103，150502（2009）]，包括最近描述的阐述[Phys.Rev.Lett. 110，250504（2013）]。我们的资源估计是基于量子计算的标准量子电路模型;它们包括电路宽度、电路深度、所采用的量子位和辅助量子位的数量、基本量子门操作的总数以及来自标准集合{X、Y、Z、H、S、T、CNOT}的每个基本容错门的更具体的门计数。为了执行这些估计，我们使用了一种方法，该方法将手动分析与通过Quipper量子编程语言和编译器生成的自动估计相结合。我们的估计涉及到示例问题大小N= 332，020，680，根据粗略的大O复杂度比较，QLSA预计比最知名的经典线性系统求解算法运行得更快。对于该问题大小，如果排除oracle成本，则期望的计算精度0.01需要近似的电路宽度340和$10^{25}$阶的电路深度，并且如果包括oracle成本，则分别需要$10^8$阶和$10^{29}$阶的电路宽度和深度，这表明通常被忽略的oracle资源是相当大的。除了提供详细的逻辑资源估计之外，本文的目的也是明确展示这些令人印象深刻的大数字是如何通过量子算法的实际电路实现而产生的。虽然我们的估计可能被证明是保守的，因为更有效的先进的量子计算技术的发展，但它们仍然提供了一个有效的基线研究目标减少的资源需求，这意味着减少了许多数量级的算法变得实用。
英文摘要：
We provide a detailed estimate for the logical resource requirements of the quantum linear system algorithm (QLSA) [Phys. Rev. Lett. 103, 150502 (2009)] including the recently described elaborations [Phys. Rev. Lett. 110, 250504 (2013)]. Our resource estimates are based on the standard quantum-circuit model of quantum computation; they comprise circuit width, circuit depth, the number of qubits and ancilla qubits employed, and the overall number of elementary quantum gate operations as well as more specific gate counts for each elementary fault-tolerant gate from the standard set {X, Y, Z, H, S, T, CNOT}. To perform these estimates, we used an approach that combines manual analysis with automated estimates generated via the Quipper quantum programming language and compiler. Our estimates pertain to the example problem size N=332,020,680 beyond which, according to a crude big-O complexity comparison, QLSA is expected to run faster than the best known classical linear-system solving algorithm. For this problem size, a desired calculation accuracy 0.01 requires an approximate circuit width 340 and circuit depth of order $10^{25}$ if oracle costs are excluded, and a circuit width and depth of order $10^8$ and $10^{29}$, respectively, if oracle costs are included, indicating that the commonly ignored oracle resources are considerable. In addition to providing detailed logical resource estimates, it is also the purpose of this paper to demonstrate explicitly how these impressively large numbers arise with an actual circuit implementation of a quantum algorithm. While our estimates may prove to be conservative as more efficient advanced quantum-computation techniques are developed, they nevertheless provide a valid baseline for research targeting a reduction of the resource requirements, implying that a reduction by many orders of magnitude is necessary for the algorithm to become practical.
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。
