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A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance

Yunfei Wang, Junyu Liu

TL;DR

This paper offers a comprehensive and unbiased review of the various concepts that have emerged in the field of quantum machine learning, which includes techniques used in Noisy Intermediate-Scale Quantum technologies and approaches for algorithms compatible with fault-tolerant quantum computing hardware.

Abstract

Quantum machine learning, which involves running machine learning algorithms on quantum devices, has garnered significant attention in both academic and business circles. In this paper, we offer a comprehensive and unbiased review of the various concepts that have emerged in the field of quantum machine learning. This includes techniques used in Noisy Intermediate-Scale Quantum (NISQ) technologies and approaches for algorithms compatible with fault-tolerant quantum computing hardware. Our review covers fundamental concepts, algorithms, and the statistical learning theory pertinent to quantum machine learning.

A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance

TL;DR

This paper offers a comprehensive and unbiased review of the various concepts that have emerged in the field of quantum machine learning, which includes techniques used in Noisy Intermediate-Scale Quantum technologies and approaches for algorithms compatible with fault-tolerant quantum computing hardware.

Abstract

Quantum machine learning, which involves running machine learning algorithms on quantum devices, has garnered significant attention in both academic and business circles. In this paper, we offer a comprehensive and unbiased review of the various concepts that have emerged in the field of quantum machine learning. This includes techniques used in Noisy Intermediate-Scale Quantum (NISQ) technologies and approaches for algorithms compatible with fault-tolerant quantum computing hardware. Our review covers fundamental concepts, algorithms, and the statistical learning theory pertinent to quantum machine learning.
Paper Structure (23 sections, 2 theorems, 14 equations, 9 figures)

This paper contains 23 sections, 2 theorems, 14 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Noisy intermediate-scale quantum (NISQ) era
  3. Variational quantum algorithm (VQA)
  4. Objective function
  5. Parameterized quantum circuits (PQC)
  6. Measurements
  7. Optimization
  8. Quantum neural tangent kernel
  9. Quantum landscapes and barren plateaus
  10. Influence of background noise
  11. Laziness
  12. Fault tolerant quantum computation (FTQC) algorithms
  13. Quantum phase estimation and quantum principle component analysis
  14. Classical algorithm framework for dequantizating QML models
  15. Harrow-Hassidim-Lloyd algorithm
  16. ...and 8 more sections

Key Result

Theorem 4.1

Shadow Tomography Theorem Shadow tomography is solvable using only $\tilde{\mathcal{O}}\left( \log^4{M} \cdot \log{D} / \varepsilon^4 \right)$ copies of the state $\rho~,$ where the $\tilde{\mathcal{O}}$ hides a higher order factor. The procedure is fully explicit.

Figures (9)

  • Figure 1: VQA in 4 parts.
  • Figure 3: Demonstration of the evolution of the loss function in the continuous limit liu2022representation. The right diagram depicts the closed-form solution when the QNTK remains constant. In contrast, the left diagram illustrates a scenario where the QNTK is nonlinear but nearly constant. In this case, representation learning is achieved, and the gradient descent equation can be addressed perturbatively.
  • Figure 4: Circuits for quantum phase estimation.
  • Figure 5: A simple illustration of principle component analysis (PCA).
  • Figure 6: Circuits for HHL algorithm morrell2023stepbystep.
  • ...and 4 more figures

Theorems & Definitions (2)

  • Theorem 4.1
  • Theorem 4.2