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Quantum-inspired classification via efficient simulation of Helstrom measurement

Wooseop Hwang, Daniel K. Park, Israel F. Araujo, Carsten Blank

Abstract

The Helstrom measurement (HM) is known to be the optimal strategy for distinguishing non-orthogonal quantum states with minimum error. Previously, a binary classifier based on classical simulation of the HM has been proposed. It was observed that using multiple copies of the sample data reduced the classification error. Nevertheless, the exponential growth in simulation runtime hindered a comprehensive investigation of the relationship between the number of copies and classification performance. We present an efficient simulation method for an arbitrary number of copies by utilizing the relationship between HM and state fidelity. Our method reveals that the classification performance does not improve monotonically with the number of data copies. Instead, it needs to be treated as a hyperparameter subject to optimization, achievable only through the method proposed in this work. We present a Quantum-Inspired Machine Learning binary classifier with excellent performance, providing such empirical evidence by benchmarking on eight datasets and comparing it with 13 hyperparameter optimized standard classifiers.

Quantum-inspired classification via efficient simulation of Helstrom measurement

Abstract

The Helstrom measurement (HM) is known to be the optimal strategy for distinguishing non-orthogonal quantum states with minimum error. Previously, a binary classifier based on classical simulation of the HM has been proposed. It was observed that using multiple copies of the sample data reduced the classification error. Nevertheless, the exponential growth in simulation runtime hindered a comprehensive investigation of the relationship between the number of copies and classification performance. We present an efficient simulation method for an arbitrary number of copies by utilizing the relationship between HM and state fidelity. Our method reveals that the classification performance does not improve monotonically with the number of data copies. Instead, it needs to be treated as a hyperparameter subject to optimization, achievable only through the method proposed in this work. We present a Quantum-Inspired Machine Learning binary classifier with excellent performance, providing such empirical evidence by benchmarking on eight datasets and comparing it with 13 hyperparameter optimized standard classifiers.
Paper Structure (1 section, 2 theorems, 32 equations, 2 figures, 1 table)

This paper contains 1 section, 2 theorems, 32 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction

Key Result

Lemma 1

Given two data points in opposing classes $a, b$ (and their encodings) and an integer $k>0$, the corresponding Helstrom operator $m_1^{a, b, k}$ is defined as Then, the eigenvalues of the operator $m_1^{a, b, k}$ are given by $\pm \lambda_{a,b,k}$ with and the operator is decomposed in

Figures (2)

  • Figure 1: Comparing F1 scores across different classifiers. This figure illustrates the predictive performance of the classifiers across all datasets utilized in this study. Within the boxes, the F1 scores, derived from cross-validation, are presented. The classifier names are abbreviated for brevity, with full names provided in the main text. All classifiers were carefully fine-tuned in terms of hyperparameters using the ax-platform.
  • Figure 2: Cross validated F1 scores vs. parameter $k$. F1 scores are shown in blue (HQCS) and red (FID). The F1 scores presented in the figures are the average of the five-fold cross validation. The maximum F1 scores, as well as the number of copies at which it occurs, are also annotated for each dataset. Results suggest non-monotonic impact of quantum copy count on prediction. HQCS+FID-classifiers perform comparably.

Theorems & Definitions (3)

  • Lemma 1
  • Proposition 1
  • proof