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arXiv 2310.05044quant-ph
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使用反卷积方法制备钟形概率分布的量子态

Quantum state preparation for bell-shaped probability distributions using deconvolution methods

Kiratholly Nandakumar Madhav Sharma, Camille de Valk, Ankur Raina, Julian van Velzen

AI总结:

本研究提出一种经典-量子混合方法,通过经典离散信号反卷积预处理拆分钟形概率质量函数,构建低深度量子电路实现态制备,支持量子硬件并行处理,在IBM量子设备上验证了两种钟形分布的加载效果。

摘要:

由于量子测量现象,量子系统是生成概率分布的天然选择。我们在自然界中从各种物理现象观测到的数据可以用量子电路建模。为了加载这种大多以概率分布形式存在的数据,我们提出了一种经典-量子混合方法。经典预处理步骤基于离散信号反卷积的概念。我们使用Jensen-Shannon距离作为代价函数,以量化经典步骤输出与目标分布的接近程度。所选代价函数具有对称性,使我们能够使用任何合适的优化算法执行反卷积步骤。反卷积步骤的输出用于构建加载给定概率分布所需的量子电路,从而整体降低电路深度。反卷积步骤将钟形概率质量函数拆分为更小的概率质量函数,这为量子硬件中的并行数据处理铺平了道路,该硬件中量子加法器电路是测量前的倒数第二步。我们在IBM Quantum模拟器和配备27量子比特处理器的IBMQ Kolkata量子计算机上测试了该算法。我们通过加载两种不同的钟形分布验证了这种经典-量子混合算法。具体而言,我们为(i)标准正态分布和(ii)拉普拉斯(Laplace)分布加载了7元素和15元素的概率质量函数(PMF)。

英文摘要:

Quantum systems are a natural choice for generating probability distributions due to the phenomena of quantum measurements. The data that we observe in nature from various physical phenomena can be modelled using quantum circuits. To load this data, which is mostly in the form of a probability distribution, we present a hybrid classical-quantum approach. The classical pre-processing step is based on the concept of deconvolution of discrete signals. We use the Jensen-Shannon distance as the cost function to quantify the closeness of the outcome from the classical step and the target distribution. The chosen cost function is symmetric and allows us to perform the deconvolution step using any appropriate optimization algorithm. The output from the deconvolution step is used to construct the quantum circuit required to load the given probability distribution, leading to an overall reduction in circuit depth. The deconvolution step splits a bell-shaped probability mass function into smaller probability mass functions, and this paves the way for parallel data processing in quantum hardware, which consists of a quantum adder circuit as the penultimate step before measurement. We tested the algorithm on IBM Quantum simulators and on the IBMQ Kolkata quantum computer, having a 27-qubit quantum processor. We validated the hybrid Classical-Quantum algorithm by loading two different distributions of bell shape. Specifically, we loaded 7 and 15-element PMF for (i) Standard Normal distribution and (ii) Laplace distribution.

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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