Quantum Machine Learning Fundamentals: Quantum Machine Learning with Qiskit

Learn how to use Qiskit as a quantum machine learning framework for building and running quantum machine learning circuits and algorithms.

1. Introduction

Quantum machine learning is an emerging field that combines quantum computing and machine learning to create novel and powerful methods for data analysis and artificial intelligence. Quantum machine learning can potentially offer significant advantages over classical machine learning, such as faster speed, lower memory requirements, and enhanced performance.

However, quantum machine learning is also a challenging and complex domain that requires a solid understanding of both quantum computing and machine learning concepts, as well as the tools and frameworks that enable their integration and implementation.

In this tutorial, you will learn how to use Qiskit as a quantum machine learning framework for building and running quantum machine learning circuits and algorithms. Qiskit is an open-source software development kit (SDK) for working with quantum computers at the level of circuits, algorithms, and applications.

Qiskit provides several modules and libraries that support quantum machine learning, such as Qiskit Aqua, Qiskit Machine Learning, and Qiskit Circuit Library. You will also explore some of the Qiskit Tutorials that demonstrate how to use Qiskit for various quantum machine learning tasks, such as classification, regression, clustering, and generative modeling.

By the end of this tutorial, you will have a basic understanding of quantum machine learning with Qiskit and how to apply it to your own data and problems. You will also be able to access more resources and examples to further your learning and practice.

Are you ready to dive into the exciting world of quantum machine learning with Qiskit? Let’s get started!

2. Quantum Machine Learning Concepts

Before you start using Qiskit for quantum machine learning, you need to have a basic understanding of some of the key concepts and principles of quantum computing and quantum machine learning. In this section, you will learn about:

• What is quantum computing and how it differs from classical computing
• What are quantum machine learning models and how they can represent and manipulate data
• What are quantum machine learning algorithms and how they can perform various tasks such as optimization, classification, and clustering

By the end of this section, you will have a solid foundation for exploring quantum machine learning with Qiskit in the next sections.

2.1. Quantum Computing Basics

Quantum computing is a paradigm of computation that uses quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computing has the potential to solve problems that are intractable or inefficient for classical computers, such as factoring large numbers, simulating quantum systems, and optimizing complex functions.

The basic unit of quantum information is called a qubit, which is a two-state quantum system that can be in a superposition of two possible values: 0 and 1. A qubit can be realized by various physical systems, such as an electron spin, a photon polarization, or a superconducting circuit. A qubit can be manipulated by applying quantum gates, which are unitary operators that change the state of the qubit. A quantum gate can be represented by a matrix, such as the Hadamard gate:

$$
H = \frac{1}{\sqrt{2}}\begin{bmatrix}
1 & 1 \\
1 & -1
\end{bmatrix}
$$

A quantum gate can also act on multiple qubits, creating entanglement between them. Entanglement is a quantum phenomenon that describes a correlation between two or more quantum systems, such that their states cannot be described independently. For example, the CNOT gate can entangle two qubits, creating a Bell state:

$$
|\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)
$$

A quantum circuit can be executed on a quantum computer, which is a device that can manipulate and measure qubits. A quantum computer can be either a physical device, such as IBM’s quantum processors, or a simulated device, such as Qiskit’s Aer simulator. A quantum computer can perform quantum algorithms, which are computational procedures that use quantum circuits to solve a problem.

One of the most famous quantum algorithms is Shor’s algorithm, which can factor a large number into its prime factors in polynomial time, whereas the best classical algorithm takes exponential time. Another important quantum algorithm is Grover’s algorithm, which can search an unsorted database in quadratic speedup, whereas the best classical algorithm takes linear time.

Quantum computing is a fascinating and rapidly evolving field that offers many opportunities and challenges for computation and information processing. If you want to learn more about quantum computing basics, you can check out the Qiskit Textbook, which is a free online resource that covers the fundamentals of quantum computing and Qiskit.

2.1. Quantum Computing Basics

Quantum computing is a paradigm of computation that uses quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computing has the potential to solve problems that are intractable or inefficient for classical computers, such as factoring large numbers, simulating quantum systems, and optimizing complex functions.

The basic unit of quantum information is called a qubit, which is a two-state quantum system that can be in a superposition of two possible values: 0 and 1. A qubit can be realized by various physical systems, such as an electron spin, a photon polarization, or a superconducting circuit. A qubit can be manipulated by applying quantum gates, which are unitary operators that change the state of the qubit. A quantum gate can be represented by a matrix, such as the Hadamard gate:

$$
H = \frac{1}{\sqrt{2}}\begin{bmatrix}
1 & 1 \\
1 & -1
\end{bmatrix}
$$

A quantum gate can also act on multiple qubits, creating entanglement between them. Entanglement is a quantum phenomenon that describes a correlation between two or more quantum systems, such that their states cannot be described independently. For example, the CNOT gate can entangle two qubits, creating a Bell state:

$$
|\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)
$$

A quantum circuit is a sequence of quantum gates applied to a set of qubits, which can be represented by a diagram, such as the following circuit that creates a Bell state:

A quantum circuit that creates a Bell state

A quantum circuit can be executed on a quantum computer, which is a device that can manipulate and measure qubits. A quantum computer can be either a physical device, such as IBM’s quantum processors, or a simulated device, such as Qiskit’s Aer simulator. A quantum computer can perform quantum algorithms, which are computational procedures that use quantum circuits to solve a problem.

One of the most famous quantum algorithms is Shor’s algorithm, which can factor a large number into its prime factors in polynomial time, whereas the best classical algorithm takes exponential time. Another important quantum algorithm is Grover’s algorithm, which can search an unsorted database in quadratic speedup, whereas the best classical algorithm takes linear time.

Quantum computing is a fascinating and rapidly evolving field that offers many opportunities and challenges for computation and information processing. If you want to learn more about quantum computing basics, you can check out the Qiskit Textbook, which is a free online resource that covers the fundamentals of quantum computing and Qiskit.

2.2. Quantum Machine Learning Models

Quantum machine learning models are mathematical frameworks that use quantum circuits to represent and manipulate data. Quantum machine learning models can exploit the quantum features of qubits, such as superposition and entanglement, to encode and process data in novel and efficient ways.

There are different types of quantum machine learning models, depending on how they interact with classical data and algorithms. Some of the main types are:

• Quantum data models: These models use quantum circuits to store and access quantum data, such as quantum states or measurements. Quantum data models can be useful for applications that involve quantum information processing, such as quantum cryptography, quantum error correction, and quantum metrology.
• Quantum-enhanced models: These models use quantum circuits to enhance classical machine learning models, such as neural networks, support vector machines, or decision trees. Quantum-enhanced models can leverage quantum algorithms, such as Grover’s or HHL, to speed up or improve the performance of classical machine learning tasks, such as optimization, classification, or regression.
• Quantum-inspired models: These models use classical circuits to mimic quantum phenomena, such as interference, phase transitions, or quantum walks. Quantum-inspired models can benefit from the insights and intuitions gained from quantum physics, without requiring a quantum computer. Quantum-inspired models can be applied to complex and noisy data, such as images, text, or graphs.

Quantum machine learning models are an active and interdisciplinary research area that aims to explore the potential and limitations of quantum computing for machine learning. If you want to learn more about quantum machine learning models, you can check out the Qiskit Global Summer School 2020, which is a free online course that covers the basics of quantum machine learning and Qiskit.

2.3. Quantum Machine Learning Algorithms

Quantum machine learning algorithms are computational procedures that use quantum circuits to perform machine learning tasks, such as optimization, classification, clustering, or generative modeling. Quantum machine learning algorithms can exploit the quantum features of qubits, such as superposition and entanglement, to achieve speedup, accuracy, or robustness over classical machine learning algorithms.

There are different types of quantum machine learning algorithms, depending on how they use quantum resources and classical data. Some of the main types are:

• Quantum variational algorithms: These algorithms use quantum circuits to encode and optimize a variational ansatz, which is a parameterized quantum state that approximates the solution of a problem. Quantum variational algorithms can be used for tasks such as quantum state preparation, quantum simulation, quantum chemistry, and quantum neural networks.
• Quantum kernel algorithms: These algorithms use quantum circuits to compute and manipulate kernel functions, which are similarity measures between data points. Quantum kernel algorithms can be used for tasks such as quantum classification, quantum regression, and quantum support vector machines.
• Quantum sampling algorithms: These algorithms use quantum circuits to sample from probability distributions that are hard to sample from classically. Quantum sampling algorithms can be used for tasks such as quantum generative modeling, quantum Boltzmann machines, and quantum recommendation systems.

Quantum machine learning algorithms are an active and interdisciplinary research area that aims to develop and analyze new methods and applications for quantum machine learning. If you want to learn more about quantum machine learning algorithms, you can check out the Qiskit Machine Learning Documentation, which is a free online resource that provides tutorials and examples on how to use Qiskit for various quantum machine learning algorithms.

3. Qiskit Overview

Qiskit is an open-source software development kit (SDK) for working with quantum computers at the level of circuits, algorithms, and applications. Qiskit provides a comprehensive and user-friendly platform for quantum computing, from writing and simulating quantum circuits to running them on real quantum devices.

Qiskit consists of four main elements:

• Qiskit Terra: This is the foundation of Qiskit, which provides the core functionality for creating and manipulating quantum circuits, executing them on different backends, and managing the results. Qiskit Terra also includes a transpiler, which optimizes and transforms quantum circuits to make them compatible with a given backend.
• Qiskit Aer: This is the element that provides high-performance simulators for quantum circuits, which can be used to test and debug quantum programs before running them on real devices. Qiskit Aer also supports noise models and noise mitigation techniques, which can help to emulate and correct the errors and imperfections of quantum hardware.
• Qiskit Ignis: This is the element that provides tools for characterizing and mitigating noise and errors in quantum devices and circuits. Qiskit Ignis can help to improve the fidelity and reliability of quantum computations by performing calibration, verification, and validation experiments.
• Qiskit Aqua: This is the element that provides a library of quantum algorithms and applications, which can be used to solve problems in various domains, such as optimization, chemistry, finance, and machine learning. Qiskit Aqua also provides a plug-in interface, which allows users to extend and customize the library with their own algorithms and applications.

Qiskit also has additional elements that build on top of the main elements, such as Qiskit Machine Learning, which provides a framework for quantum machine learning using Qiskit, and Qiskit Nature, which provides a framework for quantum natural science applications using Qiskit.

Qiskit is a powerful and versatile tool for quantum computing, which can help you to explore, develop, and run quantum programs on various platforms and devices. If you want to learn more about Qiskit, you can check out the Qiskit Documentation, which is a free online resource that provides guides, tutorials, and references on how to use Qiskit.

3.1. Qiskit Elements

Qiskit is an open-source software development kit (SDK) for working with quantum computers at the level of circuits, algorithms, and applications. Qiskit provides a comprehensive and user-friendly platform for quantum computing, from writing and simulating quantum circuits to running them on real quantum devices.

Qiskit consists of four main elements:

• Qiskit Terra: This is the foundation of Qiskit, which provides the core functionality for creating and manipulating quantum circuits, executing them on different backends, and managing the results. Qiskit Terra also includes a transpiler, which optimizes and transforms quantum circuits to make them compatible with a given backend.
• Qiskit Aer: This is the element that provides high-performance simulators for quantum circuits, which can be used to test and debug quantum programs before running them on real devices. Qiskit Aer also supports noise models and noise mitigation techniques, which can help to emulate and correct the errors and imperfections of quantum hardware.
• Qiskit Ignis: This is the element that provides tools for characterizing and mitigating noise and errors in quantum devices and circuits. Qiskit Ignis can help to improve the fidelity and reliability of quantum computations by performing calibration, verification, and validation experiments.
• Qiskit Aqua: This is the element that provides a library of quantum algorithms and applications, which can be used to solve problems in various domains, such as optimization, chemistry, finance, and machine learning. Qiskit Aqua also provides a plug-in interface, which allows users to extend and customize the library with their own algorithms and applications.

Qiskit also has additional elements that build on top of the main elements, such as Qiskit Machine Learning, which provides a framework for quantum machine learning using Qiskit, and Qiskit Nature, which provides a framework for quantum natural science applications using Qiskit.

Qiskit is a powerful and versatile tool for quantum computing, which can help you to explore, develop, and run quantum programs on various platforms and devices. If you want to learn more about Qiskit, you can check out the Qiskit Documentation, which is a free online resource that provides guides, tutorials, and references on how to use Qiskit.

3.2. Qiskit Installation and Setup

In this section, you will learn how to install and set up Qiskit on your local machine, so that you can start using it for quantum machine learning. You will also learn how to access and use the IBM Quantum Experience, which is a cloud platform that provides access to real quantum devices and simulators.

To install Qiskit, you need to have Python 3.6 or later and pip installed on your system. You can check your Python and pip versions by running the following commands in your terminal:

python --version
pip --version

If you don’t have Python or pip installed, you can download them from here and here, respectively.

Once you have Python and pip ready, you can install Qiskit by running the following command in your terminal:

pip install qiskit

This will install all the Qiskit elements and their dependencies. You can verify your installation by running the following command in your terminal:

qiskit.__qiskit_version__

This will show you the version of each Qiskit element installed on your system.

To use Qiskit, you need to import it in your Python code. You can do this by adding the following line at the beginning of your code:

import qiskit

This will allow you to access all the Qiskit modules and functions in your code.

To access and use the IBM Quantum Experience, you need to create a free account here. Once you have your account, you can log in and explore the different features and services available, such as the IBM Quantum Lab, the IBM Quantum Composer, and the IBM Quantum Systems.

To connect your Qiskit code to the IBM Quantum Experience, you need to get an API token from your account page. You can find your API token by clicking on your profile icon and selecting “My Account”. Then, you can copy your API token and save it in a file called “qiskitrc” in your home directory. The file should have the following format:

[ibmq]
token = your_api_token

This will allow you to access the IBM Quantum Experience backends from your Qiskit code. You can do this by adding the following lines to your code:

from qiskit import IBMQ
IBMQ.load_account()

This will load your account and show you the available backends. You can choose a backend and execute your quantum circuit on it by adding the following lines to your code:

backend = IBMQ.get_backend('name_of_the_backend')
job = qiskit.execute(circuit, backend)
result = job.result()

This will submit your quantum circuit to the chosen backend and return the result.

You have now learned how to install and set up Qiskit on your local machine and how to access and use the IBM Quantum Experience. You are ready to start using Qiskit for quantum machine learning. In the next section, you will learn about the Qiskit Circuit Library, which provides a collection of quantum circuits for various purposes.

3.3. Qiskit Circuit Library

The Qiskit Circuit Library is a collection of quantum circuits that can be used for various purposes, such as implementing quantum algorithms, performing quantum operations, and generating quantum states. The Qiskit Circuit Library provides a convenient and modular way to create and manipulate quantum circuits in Qiskit, without having to write them from scratch.

The Qiskit Circuit Library consists of several submodules, each containing a different category of quantum circuits. Some of the main submodules are:

• Standard Gates: This submodule contains the standard quantum gates, such as the Pauli, Hadamard, CNOT, Toffoli, and U gates. These gates can be used to build and execute any quantum circuit.
• Boolean Logic: This submodule contains the quantum circuits that implement boolean logic functions, such as AND, OR, XOR, and NOT. These circuits can be used to perform classical computations on quantum data.
• Arithmetic: This submodule contains the quantum circuits that implement arithmetic operations, such as addition, subtraction, multiplication, and division. These circuits can be used to perform numerical computations on quantum data.
• Data Structures: This submodule contains the quantum circuits that implement data structures, such as lists, arrays, stacks, and queues. These circuits can be used to store and manipulate quantum data.
• State Preparation: This submodule contains the quantum circuits that prepare quantum states, such as basis states, superposition states, entangled states, and arbitrary states. These circuits can be used to initialize and encode quantum data.
• Basis Change: This submodule contains the quantum circuits that change the basis of quantum states, such as the Fourier transform, the quantum phase estimation, and the quantum amplitude estimation. These circuits can be used to analyze and measure quantum data.
• N-Local: This submodule contains the quantum circuits that are composed of n-local blocks, which are repeated layers of single- and multi-qubit gates. These circuits can be used to construct variational ansatzes for quantum machine learning and optimization.
• Machine Learning: This submodule contains the quantum circuits that implement machine learning models, such as quantum neural networks, quantum classifiers, and quantum feature maps. These circuits can be used to perform machine learning tasks on quantum data.

The Qiskit Circuit Library is a useful and flexible tool for quantum computing, which can help you to create and customize quantum circuits in Qiskit, without having to worry about the low-level details. If you want to learn more about the Qiskit Circuit Library, you can check out the Qiskit Circuit Library Documentation, which is a free online resource that provides guides, tutorials, and references on how to use the Qiskit Circuit Library.

4. Qiskit Machine Learning

Qiskit Machine Learning is a framework for quantum machine learning using Qiskit. Qiskit Machine Learning provides tools and methods for building and running quantum machine learning circuits and algorithms, as well as integrating them with classical machine learning libraries and frameworks, such as scikit-learn, PyTorch, and TensorFlow.

Qiskit Machine Learning consists of two main modules:

• Qiskit Machine Learning Circuit: This module provides a collection of quantum circuits that can be used as building blocks for quantum machine learning models, such as quantum neural networks, quantum classifiers, and quantum feature maps. These circuits can be easily customized and combined to create complex and expressive quantum machine learning architectures.
• Qiskit Machine Learning Algorithm: This module provides a collection of quantum algorithms that can be used to perform various machine learning tasks, such as optimization, classification, regression, clustering, and generative modeling. These algorithms can leverage the quantum circuits from the Qiskit Machine Learning Circuit module, as well as the quantum algorithms from the Qiskit Aqua module.

Qiskit Machine Learning also provides a plug-in interface, which allows users to connect their quantum machine learning models and algorithms to classical machine learning libraries and frameworks, such as scikit-learn, PyTorch, and TensorFlow. This enables users to take advantage of the existing features and functionalities of these libraries and frameworks, such as data preprocessing, model evaluation, and visualization.

Qiskit Machine Learning is a powerful and flexible framework for quantum machine learning, which can help you to create and run quantum machine learning circuits and algorithms, as well as integrate them with classical machine learning libraries and frameworks. If you want to learn more about Qiskit Machine Learning, you can check out the Qiskit Machine Learning Documentation, which is a free online resource that provides guides, tutorials, and references on how to use Qiskit Machine Learning.

4.1. Qiskit Machine Learning Modules

Qiskit Machine Learning is a module of Qiskit that provides tools and functionalities for quantum machine learning. Qiskit Machine Learning is built on top of Qiskit Aqua, which is a module of Qiskit that provides tools and functionalities for quantum algorithms and applications.

Qiskit Machine Learning consists of four main submodules:

• Qiskit Machine Learning Algorithms: This submodule contains implementations of various quantum machine learning algorithms, such as variational quantum classifiers, quantum kernel methods, quantum neural networks, and quantum support vector machines. You can use these algorithms to perform tasks such as classification, regression, clustering, and generative modeling on your data.
• Qiskit Machine Learning Connectors: This submodule contains connectors that allow you to integrate Qiskit Machine Learning with popular classical machine learning frameworks, such as scikit-learn, PyTorch, and TensorFlow. You can use these connectors to leverage the features and functionalities of these frameworks, such as data preprocessing, model training, and evaluation.
• Qiskit Machine Learning Datasets: This submodule contains datasets that you can use to test and benchmark your quantum machine learning algorithms. These datasets include synthetic data, real-world data, and quantum data. You can also use your own custom datasets with Qiskit Machine Learning.
• Qiskit Machine Learning Neural Network: This submodule contains classes and interfaces that allow you to define and manipulate quantum neural networks, which are quantum circuits that can be used as machine learning models. You can use these classes and interfaces to create, train, and evaluate quantum neural networks with different architectures, activation functions, and loss functions.

Qiskit Machine Learning is a powerful and flexible module that enables you to explore and experiment with quantum machine learning. You can use Qiskit Machine Learning to create and run quantum machine learning circuits and algorithms on various quantum backends, such as simulators and real quantum devices. You can also use Qiskit Machine Learning to compare and contrast quantum machine learning with classical machine learning, and to discover the advantages and limitations of each approach.

If you want to learn more about Qiskit Machine Learning and how to use it, you can check out the Qiskit Machine Learning Documentation, which is a comprehensive online resource that covers the installation, usage, and examples of Qiskit Machine Learning.

4.2. Qiskit Machine Learning Tutorials

Qiskit Machine Learning Tutorials are a collection of Jupyter notebooks that demonstrate how to use Qiskit Machine Learning for various quantum machine learning tasks and applications. Qiskit Machine Learning Tutorials are hosted on GitHub and can be accessed online or downloaded locally.

Qiskit Machine Learning Tutorials cover a wide range of topics, such as:

• How to use Qiskit Machine Learning connectors to integrate with classical machine learning frameworks, such as scikit-learn, PyTorch, and TensorFlow.
• How to use Qiskit Machine Learning algorithms to perform classification, regression, clustering, and generative modeling on synthetic and real-world datasets.
• How to use Qiskit Machine Learning neural network to define and train quantum neural networks with different architectures and parameters.
• How to use Qiskit Machine Learning datasets to load and preprocess quantum and classical data for quantum machine learning.
• How to use Qiskit Machine Learning to compare and benchmark quantum machine learning with classical machine learning.

Qiskit Machine Learning Tutorials are designed to be interactive and easy to follow. You can run the code cells, modify the parameters, and observe the results. You can also add your own code cells, comments, and notes to customize the tutorials to your needs and preferences.

Qiskit Machine Learning Tutorials are a great way to learn by doing and to gain hands-on experience with quantum machine learning with Qiskit. You can use the tutorials as a starting point for your own projects and experiments, or as a reference for your own questions and challenges.

If you want to access the Qiskit Machine Learning Tutorials, you can visit the Qiskit Machine Learning Tutorials GitHub repository, where you can find the links to the online versions, the instructions for the local installation, and the list of the available tutorials.

5. Conclusion

In this tutorial, you have learned how to use Qiskit as a quantum machine learning framework for building and running quantum machine learning circuits and algorithms. You have also learned some of the key concepts and principles of quantum computing and quantum machine learning, and how they differ from classical computing and machine learning.

You have explored the various modules and libraries that Qiskit provides to support quantum machine learning, such as Qiskit Aqua, Qiskit Machine Learning, and Qiskit Circuit Library. You have also seen some of the Qiskit Tutorials that demonstrate how to use Qiskit for various quantum machine learning tasks and applications, such as classification, regression, clustering, and generative modeling.

By following this tutorial, you have gained a basic understanding of quantum machine learning with Qiskit and how to apply it to your own data and problems. You have also acquired some practical skills and experience with quantum machine learning that you can use to further your learning and practice.

Quantum machine learning is an exciting and rapidly evolving field that offers many opportunities and challenges for computation and artificial intelligence. Qiskit is a powerful and flexible framework that enables you to explore and experiment with quantum machine learning in an easy and accessible way. We hope that this tutorial has inspired you to continue your journey with quantum machine learning and Qiskit, and to discover the potential and limitations of this emerging paradigm.

Thank you for reading this tutorial and happy learning!