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

TL;DR

This paper introduces a quadratic formulation of mutual information for sensor placement optimization, enabling the use of Ising and quantum annealing machines to efficiently select sensors for maximum information gain.

Contribution

It proposes a novel QUBO formulation of mutual information for sensor placement, facilitating quantum annealing solutions for larger sensor networks.

Findings

Quantum annealing produced reasonable sensor placement solutions.

The method scales to any number of sensors.

Quantum advantage expected with larger sensor sets.

Abstract

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.