Empirical Power of Quantum Encoding Methods for Binary Classification

TL;DR

The work tackles how quantum data encodings influence binary classification performance by evaluating five feature maps within a QSVC framework against a classical LightGBM baseline on four real-world datasets. It combines quantum feature selection via a QUBO formulation with fixed-parameter QSVC to isolate encoding effects, revealing that IQP encoding often matches LightGBM while other encodings vary in performance. A key contribution is demonstrating statistical equivalence between IQP and LightGBM across multiple metrics, suggesting a kernel-like role for quantum encodings and potential quantum advantages in data-limited settings. The study also provides insights into expressibility of different feature maps and the limited impact of entanglement within the QSVC architecture, guiding future encoding choices and avenues for deeper IQP-focused investigations.

Abstract

Quantum machine learning is one of the many potential applications of quantum computing, each of which is hoped to provide some novel computational advantage. However, quantum machine learning applications often fail to outperform classical approaches on real-world classical data. The ability of these models to generalize well from few training data points is typically considered one of the few definitive advantages of this approach. In this work, we will instead focus on encoding schemes and their effects on various machine learning metrics. Specifically, we focus on real-world data encoding to demonstrate differences between quantum encoding strategies for several real-world datasets and the classification model standard, LightGBM. In particular, we apply the following encoding strategies, including three standard approaches and two modified approaches: Angle, Amplitude, IQP, Entangled Angle, and Alternative IQP. As these approaches require either a significant number of qubits or gates to encode larger datasets, we perform feature selection to support the limited computing power of quantum simulators. This feature selection is performed through a quantum annealing enhanced approach that builds on a QUBO formulation of the problem. In this work, we provide a preliminary demonstration that quantum machine learning with the IQP encoding and LightGBM produce statistically equivalent results for a large majority of the assigned learning tasks.

Figures (8)

• Figure 1: Pearson correlation scores of the features for each respective dataset.
• Figure 2: Two-qubit Entangled Angle example
• Figure 3: This is an example on how to amplitude encode data: (a) displays the binary tree decomposition of $( \sqrt{.2}, \sqrt{.4}, \sqrt{.3}, \sqrt{.1})$, and (b) is the respective circuit to encode the binary tree.
• Figure 4: The aggregated results of the experiments are collected. Each column consists of a data set with the accuracy, F1 score, and AUC score described in box plots.
• Figure 5: General circuit of the fidelity test for an arbitrary feature map for data points $d_i$ and $d_j$.