Quantum Annealing Feature Selection on Light-weight Medical Image Datasets

TL;DR

This work presents a method to solve larger feature selection instances than previously demonstrated on commercial quantum annealers, combining a linear Ising penalty mechanism with subsampling and thresholding techniques to enhance scalability and compare it against a range of feature selection strategies.

Abstract

We investigate the use of quantum computing algorithms on real quantum hardware to tackle the computationally intensive task of feature selection for light-weight medical image datasets. Feature selection is often formulated as a k of n selection problem, where the complexity grows binomially with increasing k and n. As problem sizes grow, classical approaches struggle to scale efficiently. Quantum computers, particularly quantum annealers, are well-suited for such problems, offering potential advantages in specific formulations. We present a method to solve larger feature selection instances than previously presented on commercial quantum annealers. Our approach combines a linear Ising penalty mechanism with subsampling and thresholding techniques to enhance scalability. The method is tested in a toy problem where feature selection identifies pixel masks used to reconstruct small-scale medical images. The results indicate that quantum annealing-based feature selection is effective for this simplified use case, demonstrating its potential in high-dimensional optimization tasks. However, its applicability to broader, real-world problems remains uncertain, given the current limitations of quantum computing hardware.

Figures (5)

• Figure 1: Illustration of the feature selection process using quantum annealing, or classically, to extract pixels and train a convolutional decoder for reconstruction.
• Figure 2: (Left) A part of the Pegasus topology implemented in the quantum annealing D-Wave Advantage_system4.1 architecture, where qubits (blue circles) are connected with couplings (black lines) to a maximum of 15 other qubits. (Right) Anneal schedule parameters, where $A(s)$ and $B(s)$ scale the transverse field and Ising contributions, respectively. These coefficients are functions of the parameter $s \in [0,1]$, which depends on the physical time $t$.
• Figure 3: Feature selection pipeline: Images are flattened to compute the importance and redundancy terms, which are combined into the QUBO. The $k$ of $n$ constraint is enforced via a linear penalty or a quadratic constraint (Fig. \ref{['fig:constraint']}). Then, the QUBO is solved using classical or quantum solvers.
• Figure 4: Illustration of the conventional quadratic constraint to enforce selecting $k$ of $n$ features, which is infeasible due to limited connectivity on the annealer. When dealing with a sparsified QUBO, we propose a linear Ising penalty to enforce the constraint. The QUBO and its constraint are shown, along with a plot of the optimization energy (y-axis) against the Hamming weight (x-axis), indicating how many features are selected.
• Figure 5: Visual comparison of images from the test set, overlayed with the selected pixels (top row) and the decoder reconstructed images from the selected pixels.