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arXiv 2109.09685quant-ph
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囚禁离子量子计算机上的低深度振幅估计

Low depth amplitude estimation on a trapped ion quantum computer

Tudor Giurgica-Tiron, Sonika Johri, Iordanis Kerenidis, Jason Nguyen, Neal Pisenti, Anupam Prakash, Ksenia Sosnova, Ken Wright, William Zeng

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摘要：

振幅估计是一种基本的量子算法原语，它使量子计算机能够为一大类统计估计问题（包括蒙特卡罗方法）实现二次加速。从近期硬件实现的角度来看，主要缺点是幅度估计算法需要非常深的量子线路。最近的工作已经成功地在一定程度上减少了这些算法所需的资源，通过权衡一些较低深度电路的加速，但仍然需要高质量的量子位来演示这些算法。在这里，我们报告的结果的实验演示的振幅估计的国家的最先进的囚禁离子量子计算机。振幅估计算法用于估计随机选择的四维单位向量的内积，并且基于极大似然估计（MLE）和中国剩余定理（CRT）技术。当考虑更深的量子线路时，观察到基于MLE的方法的准确度的显著改善，包括具有超过90个两量子位门和深度60的电路，实现了$10^{-2}$量级的平均加性估计误差。发现基于CRT的方法为许多数据点提供了准确的估计，但平均而言对噪声的鲁棒性较低。最后，我们分析了两个幅度估计算法，考虑到硬件噪声的具体情况，以进一步改善结果。

英文摘要：

Amplitude estimation is a fundamental quantum algorithmic primitive that enables quantum computers to achieve quadratic speedups for a large class of statistical estimation problems, including Monte Carlo methods. The main drawback from the perspective of near term hardware implementations is that the amplitude estimation algorithm requires very deep quantum circuits. Recent works have succeeded in somewhat reducing the necessary resources for such algorithms, by trading off some of the speedup for lower depth circuits, but high quality qubits are still needed for demonstrating such algorithms. Here, we report the results of an experimental demonstration of amplitude estimation on a state-of-the-art trapped ion quantum computer. The amplitude estimation algorithms were used to estimate the inner product of randomly chosen four-dimensional unit vectors, and were based on the maximum likelihood estimation (MLE) and the Chinese remainder theorem (CRT) techniques. Significant improvements in accuracy were observed for the MLE based approach when deeper quantum circuits were taken into account, including circuits with more than ninety two-qubit gates and depth sixty, achieving a mean additive estimation error on the order of $10^{-2}$. The CRT based approach was found to provide accurate estimates for many of the data points but was less robust against noise on average. Last, we analyze two more amplitude estimation algorithms that take into account the specifics of the hardware noise to further improve the results.

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。

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