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arXiv 2407.14747quant-ph
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使用 Ising 和量子退火机进行传感器放置优化的互信息二次形式

Quadratic Formulation of Mutual Information for Sensor Placement Optimization using Ising and Quantum Annealing Machines

Yuta Nakano, Shigeyasu Uno

AI总结:

针对传感器放置组合优化问题,提出将多元正态分布假设下选定与其余传感器位置间的互信息形式化为QUBO问题,并利用量子退火机求解验证,为大规模传感器优化提供了新方法。

摘要:

我们解决了一个组合优化问题,旨在从多个候选位置中确定预定数量传感器的放置,以用最少数量的传感器最大化信息获取。假设来自传感器放置预定候选位置的数据遵循多元正态分布,我们将选定传感器位置的数据与其他位置数据之间的互信息(MI)定义为目标函数,并通过我们提出的方法将其形式化为二次无约束二值优化(QUBO)问题。作为示例,我们使用量子退火机计算了3个传感器放置候选位置的目标函数最优解,并确认所获得的结果是合理的。我们提出的形式化方法可应用于任意数量的传感器,并且预计随着传感器数量的增加,量子退火的优势将会显现。

英文摘要:

We address a combinatorial optimization problem to determine the placement of a predefined number of sensors from multiple candidate positions, aiming to maximize information acquisition with the minimum number of sensors. Assuming that the data from predefined candidates of sensor placements follow a multivariate normal distribution, we defined mutual information (MI) between the data from selected sensor positions and the data from the others as an objective function, and formulated it in a Quadratic Unconstrainted Binary Optimization (QUBO) problem by using a method we proposed. As an example, we calculated optimal solutions of the objective functions for 3 candidates of sensor placements using a quantum annealing machine, and confirmed that the results obtained were reasonable. The formulation method we proposed can be applied to any number of sensors, and it is expected that the advantage of quantum annealing emerges as the number of sensors increases.

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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