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Learning to Measure Quantum Neural Networks

Samuel Yen-Chi Chen, Huan-Hsin Tseng, Hsin-Yi Lin, Shinjae Yoo

TL;DR

The paper tackles the limitation of fixed measurement observables in quantum neural networks by introducing an end-to-end differentiable framework that learns a Hermitian observable $B$ together with the variational circuit parameters. By parameterizing $B$ with $N^2$ real coefficients and optimizing it jointly with the circuit, the approach expands the spectral range of measurements and improves task performance, as demonstrated on classification (make_moons) and speaker recognition (VCTK). The experiments show that learnable measurements, especially when paired with separate optimizers for observables and gates, yield the best results, indicating greater expressivity and adaptability of QNNs. This work advances automated design in quantum machine learning by treating measurements as trainable components inside a differentiable pipeline, with potential for broader QML applications.

Abstract

The rapid progress in quantum computing (QC) and machine learning (ML) has attracted growing attention, prompting extensive research into quantum machine learning (QML) algorithms to solve diverse and complex problems. Designing high-performance QML models demands expert-level proficiency, which remains a significant obstacle to the broader adoption of QML. A few major hurdles include crafting effective data encoding techniques and parameterized quantum circuits, both of which are crucial to the performance of QML models. Additionally, the measurement phase is frequently overlooked-most current QML models rely on pre-defined measurement protocols that often fail to account for the specific problem being addressed. We introduce a novel approach that makes the observable of the quantum system-specifically, the Hermitian matrix-learnable. Our method features an end-to-end differentiable learning framework, where the parameterized observable is trained alongside the ordinary quantum circuit parameters simultaneously. Using numerical simulations, we show that the proposed method can identify observables for variational quantum circuits that lead to improved outcomes, such as higher classification accuracy, thereby boosting the overall performance of QML models.

Learning to Measure Quantum Neural Networks

TL;DR

The paper tackles the limitation of fixed measurement observables in quantum neural networks by introducing an end-to-end differentiable framework that learns a Hermitian observable together with the variational circuit parameters. By parameterizing with real coefficients and optimizing it jointly with the circuit, the approach expands the spectral range of measurements and improves task performance, as demonstrated on classification (make_moons) and speaker recognition (VCTK). The experiments show that learnable measurements, especially when paired with separate optimizers for observables and gates, yield the best results, indicating greater expressivity and adaptability of QNNs. This work advances automated design in quantum machine learning by treating measurements as trainable components inside a differentiable pipeline, with potential for broader QML applications.

Abstract

The rapid progress in quantum computing (QC) and machine learning (ML) has attracted growing attention, prompting extensive research into quantum machine learning (QML) algorithms to solve diverse and complex problems. Designing high-performance QML models demands expert-level proficiency, which remains a significant obstacle to the broader adoption of QML. A few major hurdles include crafting effective data encoding techniques and parameterized quantum circuits, both of which are crucial to the performance of QML models. Additionally, the measurement phase is frequently overlooked-most current QML models rely on pre-defined measurement protocols that often fail to account for the specific problem being addressed. We introduce a novel approach that makes the observable of the quantum system-specifically, the Hermitian matrix-learnable. Our method features an end-to-end differentiable learning framework, where the parameterized observable is trained alongside the ordinary quantum circuit parameters simultaneously. Using numerical simulations, we show that the proposed method can identify observables for variational quantum circuits that lead to improved outcomes, such as higher classification accuracy, thereby boosting the overall performance of QML models.
Paper Structure (11 sections, 6 equations, 7 figures)

This paper contains 11 sections, 6 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Quantum Neural Networks
  4. Learnable Quantum Measurements
  5. Experiments
  6. Task 1: Classification
  7. Task 2: Speaker Recognition
  8. Data
  9. Model architecture
  10. Results
  11. Conclusion

Figures (7)

  • Figure 1: Hybrid Quantum-Classical Computing with Learnable Measurements.
  • Figure 2: Generic Structure of a Variational Quantum Circuit (VQC).
  • Figure 3: Comparison of different VQC models in make_moons dataset with noise = 0.1.
  • Figure 4: Comparison of different VQC models in make_moons dataset with noise = 0.2.
  • Figure 5: Comparison of different VQC models in make_moons dataset with noise = 0.3.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Definition 1