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The Impact of Feature Embedding Placement in the Ansatz of a Quantum Kernel in QSVMs

Ilmo Salmenperä, Ilmars Kuhtarskis, Arianne Meijer van de Griend, Jukka K. Nurminen

TL;DR

This work study and categorize various architectural patterns in QEKs and show that existing architectural styles do not behave as the literature supposes, and produces a novel alternative architecture based on the old ones that performs equally well while containing fewer gates than its older counterparts.

Abstract

Designing a useful feature map for a quantum kernel is a critical task when attempting to achieve an advantage over classical machine learning models. The choice of circuit architecture, i.e. how feature-dependent gates should be interwoven with other gates is a relatively unexplored problem and becomes very important when using a model of quantum kernels called Quantum Embedding Kernels (QEK). We study and categorize various architectural patterns in QEKs and show that existing architectural styles do not behave as the literature supposes. We also produce a novel alternative architecture based on the old ones and show that it performs equally well while containing fewer gates than its older counterparts.

The Impact of Feature Embedding Placement in the Ansatz of a Quantum Kernel in QSVMs

TL;DR

This work study and categorize various architectural patterns in QEKs and show that existing architectural styles do not behave as the literature supposes, and produces a novel alternative architecture based on the old ones that performs equally well while containing fewer gates than its older counterparts.

Abstract

Designing a useful feature map for a quantum kernel is a critical task when attempting to achieve an advantage over classical machine learning models. The choice of circuit architecture, i.e. how feature-dependent gates should be interwoven with other gates is a relatively unexplored problem and becomes very important when using a model of quantum kernels called Quantum Embedding Kernels (QEK). We study and categorize various architectural patterns in QEKs and show that existing architectural styles do not behave as the literature supposes. We also produce a novel alternative architecture based on the old ones and show that it performs equally well while containing fewer gates than its older counterparts.
Paper Structure (10 sections, 6 equations, 7 figures)

This paper contains 10 sections, 6 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Methodology
  4. Quantum Embedding Kernels
  5. Quantum kernel architectures
  6. Experimental setup
  7. Results
  8. Discussion
  9. Conclusion
  10. Ansatz structure

Figures (7)

  • Figure 1: Three different architectural solutions: (a) data-first structure, (b) data-last structure, (c) the data-weaved structure. $F$ is feature-dependant layer and $P_n$ is the n:th parameterized layer. Note that the data-weaved structure has one extra feature-dependent layer before the other layers.
  • Figure 2: Two methods for computing the inner product of the kernel: (a) Loschmidt echo test and (b) Swap test
  • Figure 3: Box plot of test set accuracies of the three kernel architectures on four different datasets. Models are labelled as: DW - Data-weaved, DF - Data-first and DL - Data-last. The green diamond is the mean accuracy of the 25 models, while the red bar is the median accuracy. White dots represent outlier data points in the accuracy. The results are grouped together by the amount of parameter layers in the architecture, indicated by the number after the label. All the results were gained from the same test training split.
  • Figure 4: Mean target-alignment values as the function of time for different datasets and layers. Red dashed line represents the data-weaved architecture, green dotted line represents the data-first architecture and blue solid line represents the data-last architecture. The lines are grouped together by the amount of parameter layers in the architecture.
  • Figure 5: Average test accuracy for 25 different models over training iterations for the data-weaved model (The red dashed line) and the data-last model (blue solid line). The data-first model was omitted due to it being identical to the data-weaved model with one less parameter layer.
  • ...and 2 more figures