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QMetric: Benchmarking Quantum Neural Networks Across Circuits, Features, and Training Dimensions

Silvie Illésová, Tomasz Rybotycki, Martin Beseda

TL;DR

QMetric is presented, a Python package offering a suite of interpretable metrics to evaluate quantum circuit expressibility, feature representations, and training dynamics, which quantifies key aspects such as circuit fidelity, entanglement entropy, barren plateau risk, and training stability.

Abstract

As hybrid quantum-classical models gain traction in machine learning, there is a growing need for tools that assess their effectiveness beyond raw accuracy. We present QMetric, a Python package offering a suite of interpretable metrics to evaluate quantum circuit expressibility, feature representations, and training dynamics. QMetric quantifies key aspects such as circuit fidelity, entanglement entropy, barren plateau risk, and training stability. The package integrates with Qiskit and PyTorch, and is demonstrated via a case study on binary MNIST classification comparing classical and quantum-enhanced models. Code, plots, and a reproducible environment are available on GitLab.

QMetric: Benchmarking Quantum Neural Networks Across Circuits, Features, and Training Dimensions

TL;DR

QMetric is presented, a Python package offering a suite of interpretable metrics to evaluate quantum circuit expressibility, feature representations, and training dynamics, which quantifies key aspects such as circuit fidelity, entanglement entropy, barren plateau risk, and training stability.

Abstract

As hybrid quantum-classical models gain traction in machine learning, there is a growing need for tools that assess their effectiveness beyond raw accuracy. We present QMetric, a Python package offering a suite of interpretable metrics to evaluate quantum circuit expressibility, feature representations, and training dynamics. QMetric quantifies key aspects such as circuit fidelity, entanglement entropy, barren plateau risk, and training stability. The package integrates with Qiskit and PyTorch, and is demonstrated via a case study on binary MNIST classification comparing classical and quantum-enhanced models. Code, plots, and a reproducible environment are available on GitLab.

Paper Structure

This paper contains 30 sections, 16 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Software Specifications
  3. Metrics Categories
  4. Quantum Circuit Metrics
  5. Quantum Circuit Expressibility
  6. Quantum Circuit Fidelity
  7. Quantum Locality Ratio
  8. Effective Entanglement Entropy
  9. Quantum Mutual Information
  10. Quantum Feature Space Metrics
  11. Feature Map Compression Ratio
  12. Effective Dimension of Quantum Feature Space
  13. Quantum Layer Activation Diversity
  14. Quantum Output Sensitivity
  15. Training Dynamics
  16. ...and 15 more sections

Figures (2)

  • Figure 1: Hybrid quantum-classical model architecture. Classical inputs are encoded into quantum states via a feature map and processed by a parameterized circuit. The quantum output is passed to a classical linear layer and sigmoid activation for binary classification.
  • Figure 2: Architecture of the classical baseline neural network. A fully connected feedforward model processes PCA-reduced MNIST inputs to perform binary classification between digits 0 and 1.