[Paper Review] Quantum machine learning for data scientists

Dawid Kopczyk|arXiv (Cornell University)|Apr 25, 2018

Quantum Computing Algorithms and Architecture24 references63 citations

TL;DR

The paper surveys quantum algorithms (e.g., Grover’s search, quantum minimization, quantum Fourier transform, and quantum phase estimation) and discusses how quantum parallelism enables faster data-processing steps in quantum machine learning, with illustrative examples.

ABSTRACT

This text aims to present and explain quantum machine learning algorithms to a data scientist in an accessible and consistent way. The algorithms and equations presented are not written in rigorous mathematical fashion, instead, the pressure is put on examples and step by step explanation of difficult topics. This contribution gives an overview of selected quantum machine learning algorithms, however there is also a method of scores extraction for quantum PCA algorithm proposed as well as a new cost function in feed-forward quantum neural networks is introduced. The text is divided into four parts: the first part explains the basic quantum theory, then quantum computation and quantum computer architecture are explained in section two. The third part presents quantum algorithms which will be used as subroutines in quantum machine learning algorithms. Finally, the fourth section describes quantum machine learning algorithms with the use of knowledge accumulated in previous parts.

Motivation & Objective

• Motivate the use of quantum algorithms as subroutines for quantum machine learning.
• Introduce key quantum algorithms and their potential speedups over classical counterparts.
• Explain how quantum parallelism and oracle-based queries enable efficient data processing in quantum circuits.

Proposed method

• Describe Grover’s search algorithm and its quadratic speedup over classical search.
• Explain the construction of a quantum oracle and its role in marking desired inputs.
• Illustrate the amplitude amplification (inversion about the mean) step in Grover’s iterations.
• Discuss other foundational quantum algorithms (quantum minimization, quantum Fourier transform, quantum phase estimation) and their roles as subroutines for quantum ML.
• Provide a high-level view of time complexity using big-O notation to compare quantum and classical approaches.

Experimental results

Research questions

• RQ1 What advantages do fundamental quantum algorithms offer as building blocks for quantum machine learning?
• RQ2 How do quantum oracles and amplitude amplification translate into practical speedups for searching or optimizing input spaces?
• RQ3 What are the typical time complexity implications of using these quantum subroutines in ML workflows?

Key findings

• Quantum algorithms can achieve quadratic or exponential speedups over classical counterparts in certain problem classes.
• Grover’s algorithm uses a quantum oracle to identify marked inputs with high probability in O(√N) iterations for N inputs.
• Quantum amplitude amplification enhances the probability of measuring the desired state after oracle applications.
• Foundational algorithms like QFT and phase estimation underpin quantum ML tasks such as data encoding and parameter estimation.
• The document provides example-driven explanations of implementing quantum gates and circuits for these algorithms.