Benchmark of the Full and Reduced Effective Resistance Kernel for Molecular Classification

TL;DR

This paper evaluates the effective resistance kernel for molecular classification, demonstrating quantum speedups and efficiency improvements with a focus on balancing accuracy and computational complexity.

Contribution

It introduces methodical improvements to the commute time kernel, explores quantum speedups, and benchmarks on chemistry datasets, highlighting efficiency over accuracy.

Findings

Quantum speedup in kernel computation

Efficiency gains in runtime without large accuracy loss

Effective for chemistry datasets with large data points

Abstract

We present a comprehensive study of the commute time kernel method via the effective resistance framework analyzing the quantum complexity of the originally classical approach. Our study reveals that while there is a trade-off between accuracy and computational complexity, significant improvements can be achieved in terms of runtime efficiency without substantially compromising on precision. Our investigation highlights a notable quantum speedup in calculating the kernel, which offers a quadratic improvement in time complexity over classical approaches in certain instances. In addition, we introduce methodical improvements over the original work on the commute time kernel and provide empirical evidence suggesting the potential reduction of kernel queries without significant impact on result accuracy. Benchmarking our method on several chemistry-based datasets: $\tt{AIDS}$, $\tt{NCL1}$, $\tt{PTC-MR}$, $\tt{MUTAG}$, $\tt{PROTEINS}$ - data points previously unexplored in existing literature, shows that while not always the most accurate, it excels in time efficiency. This makes it a compelling alternative for applications where computational speed is crucial. Our results highlight the balance between accuracy, computational complexity, and speedup offered by quantum computing, promoting further research into efficient algorithms for kernel methods and their applications in chemistry-based datasets.