A Brief Introduction to Quantum Machine Learning Techniques

You may have heard of Quantum Computing and must have heard of Machine Learning. Quantum Machine Learning or QML explores how to use Quantum techniques to do Machine Learning, learn patterns, and discover information.

What is Machine Learning?

The value of many techniques in Machine Learning is their ability to learn from new data. Historically, a computer program could do only as programmed – following a set of rules. Machine Learning is not new, but the emphasis is. Machine Learning has leaped forward using Deep Learning Neural Networks to learn patterns. But here, we will outline some of the more straightforward techniques and how these can be applied in the Quantum Domain. Essentially, the machine covers techniques at the simple end, such as least squares and regression, to later LSTM models. There are some outstanding books on Machine Learning available in our book section.

Supervised Learning

Supervised learning algorithms are trained using labeled data, where the correct output is provided during training. The algorithm makes predictions or decisions based on input data and is corrected when its predictions are wrong.

• Linear Regression: Used for predicting a continuous value. For example, they predict house prices based on size and location.
• Logistic Regression: Used for binary classification tasks, such as spam detection or determining if a customer will buy a product.
• Decision Trees: A model that makes decisions based on asking a series of questions based on the features of the input data. Useful in both classification and regression tasks.
• Random Forests: An ensemble method that uses multiple decision trees to improve prediction accuracy and control over-fitting.
• Support Vector Machines (SVM): Designed for binary classification tasks. SVM finds the hyperplane that best separates different classes in the feature space.
• Neural Networks: These are layers of nodes that can learn complex patterns through backpropagation. Compelling in handling large and complex datasets.

Unsupervised Learning

Unsupervised learning involves training algorithms on data without labeled responses, allowing the model to independently identify patterns and relationships in the data.

• Clustering (e.g., K-means, Hierarchical clustering): Used to group data points into clusters where points in the same cluster are more similar than those in other clusters.
• Principal Component Analysis (PCA): A dimensionality reduction technique that transforms data into fewer dimensions while retaining most of the variation in the data.
• Autoencoders: Neural networks designed to compress input into a lower-dimensional code and then reconstruct the output from this representation.

Reinforcement Learning

Reinforcement learning algorithms learn to make decisions by acting in an environment to achieve a goal. The learner is not told which actions to take but must discover which ones yield the most reward by trying them.

• Q-learning: A model-free reinforcement learning algorithm that learns the value of an action in a particular state.
• Deep Q-Networks (DQN): Combines Q-learning with deep neural networks, allowing it to handle high-dimensional sensory input.

Semi-supervised and Self-supervised Learning

These intermediate forms of learning use both labeled and unlabeled data for training, typically using a small amount of labeled data and a large amount of unlabeled data.

• Semi-supervised Learning: Combines a small amount of labeled data with a large amount of unlabeled data during training. It’s useful when labeling data is expensive or laborious.
• Self-supervised Learning: A form of unsupervised learning where the data provides supervision. It’s often used when pre-training models on a large corpus of unlabeled data can be fine-tuned on a smaller labeled dataset.

Ensemble Methods

Ensemble methods combine the predictions from multiple machine learning algorithms to produce a more accurate prediction than any individual model.

• Boosting (e.g., AdaBoost, Gradient Boosting): Combines multiple weak learners into a strong learner. Each model in the sequence focuses on correctly predicting the instances misclassified by the previous model.
• Bagging (e.g., Bootstrap Aggregating): Improves the stability and accuracy of machine learning algorithms by combining multiple models, reducing variance, and avoiding overfitting.

Quantum Computing 101

At the heart of quantum computing is the quantum bit or qubit, which, unlike a classical bit that can be either 0 or 1, can exist in a state of 0, 1, or both simultaneously, due to superposition. This capability, along with entanglement—where the state of one qubit can depend on the state of another, no matter the distance between them—allows quantum computers to perform complex calculations more efficiently than their classical counterparts for specific tasks.

Quantum Algorithms

Quantum Machine Learning (QML), an Introduction

Quantum Machine Learning (QML) is an emerging field that combines quantum computing with machine learning algorithms. By leveraging the principles of quantum mechanics, QML algorithms aim to solve complex computational problems more efficiently than their classical counterparts. Below, I’ll introduce several notable QML algorithms, providing an overview and detailed explanation for each.

Many researchers around the planet are looking at how they can apply the knowledge generated in the classical machine-learning world and transfer it to the Quantum domain. We’ll explore some simple techniques and how classical algorithms can function when, instead of classical registers, we have Qubit registers.

Quantum Support Vector Machine (QSVM)

The Quantum Support Vector Machine (QSVM) is an adaptation of the classical support vector machine algorithm, designed to run on quantum computers. It aims to classify data by finding the optimal separating hyperplane in a high-dimensional space, leveraging quantum computing’s ability to handle complex calculations efficiently.

Explanation and Technique

QSVM utilizes quantum circuits to map classical data into a high-dimensional quantum feature space, a process known as quantum feature mapping. This mapping is more efficient on a quantum computer due to its ability to exploit quantum superposition and entanglement. The algorithm then finds the separating hyperplane in this quantum feature space, potentially offering exponential speedup in feature space exploration compared to classical SVMs. The quantum kernel estimation technique is a key component, allowing the computation of inner products in the feature space implicitly, without needing to compute the feature map explicitly.

Quantum Principal Component Analysis (QPCA)

Quantum Principal Component Analysis (QPCA) is a quantum algorithm designed to perform principal component analysis (PCA), a widely used technique in classical machine learning for dimensionality reduction, more efficiently.

Explanation and Technique

QPCA leverages quantum phase estimation and quantum singular value decomposition to identify the principal components of a dataset. By encoding the data into a quantum state and applying these quantum algorithms, QPCA can theoretically achieve exponential speedup in identifying the most significant features of the data. This makes it particularly useful for handling large datasets where classical PCA would be computationally expensive.

Variational Quantum Eigensolver (VQE)

The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm designed to find the eigenvalues of a Hamiltonian, which is particularly useful in quantum chemistry and physics simulations.

Explanation and Technique

VQE combines quantum computing’s ability to efficiently represent and manipulate quantum states with classical optimization techniques. A parameterized quantum circuit, known as an ansatz, is used to prepare quantum states that approximate the ground state of a Hamiltonian. Classical computers then optimize these parameters to minimize the energy expectation value, iteratively improving the quantum state’s approximation. This hybrid approach allows VQE to be run on current quantum hardware, making it one of the most promising algorithms for near-term quantum applications.

Quantum Approximate Optimization Algorithm (QAOA)

The Quantum Approximate Optimization Algorithm (QAOA) is designed to solve combinatorial optimization problems, which are notoriously challenging for classical computers. It represents a hybrid quantum-classical approach, aiming to find approximate solutions to optimization problems by leveraging the principles of quantum superposition and entanglement.

Explanation and Technique

QAOA works by encoding the optimization problem into a cost Hamiltonian, whose ground state corresponds to the optimal solution. The algorithm then uses a parameterized quantum circuit to prepare states that approximate this ground state. The parameters are optimized through a classical routine to minimize the expectation value of the cost Hamiltonian, iteratively improving the solution’s approximation. This approach is particularly notable for its potential to provide speedups for specific optimization problems and its suitability for near-term quantum devices.

Quantum Boltzmann Machine (QBM)

Quantum Boltzmann Machines (QBMs) are quantum versions of the classical Boltzmann machines, a type of stochastic recurrent neural network. QBMs aim to leverage quantum computing to enhance the efficiency and capacity of learning complex distributions.

Explanation and Technique

QBMs utilize quantum systems to represent the Boltzmann distribution, with quantum bits (qubits) encoding the states of neurons. The quantum nature of these systems allows for the representation of complex probability distributions with fewer resources than classical systems. Quantum superposition and entanglement enable the exploration of the solution space more efficiently, potentially offering significant advantages in learning complex patterns and correlations in data.

Quantum Neural Networks (QNNs)

Quantum Neural Networks (QNNs) extend the concept of neural networks into the quantum domain, aiming to combine quantum computing’s strengths with the adaptability and learning capabilities of neural networks.

Explanation and Technique

QNNs are composed of layers of quantum gates that act as neurons, processing quantum information through complex transformations. These networks can exploit quantum parallelism to process information in ways that are fundamentally different from classical neural networks. The parameters of the quantum gates (analogous to weights in classical neural networks) are optimized to perform specific tasks, such as classification or pattern recognition. The potential of QNNs lies in their ability to handle high-dimensional data with fewer parameters and to perform computations that are intractable for classical systems.

These algorithms illustrate the innovative ways in which quantum computing is being applied to machine learning, offering glimpses into a future where quantum-enhanced algorithms could solve problems beyond the reach of classical computation. As research in this field progresses, we can expect to see further advancements and refinements in these algorithms, expanding their applicability and efficiency.

QML References

• Peruzzo, A., McClean, J., Shadbolt, P., Yung, M.-H., Zhou, X.-Q., Love, P. J., Aspuru-Guzik, A., & O’Brien, J. L. (2014). “A variational eigenvalue solver on a photonic quantum processor,” Nature Communications, 5, 4213. This paper introduces the VQE, demonstrating its application in solving quantum chemistry problems on early quantum processors.
• Havlíček, V., Córcoles, A. D., Temme, K., Harrow, A. W., Kandala, A., Chow, J. M., & Gambetta, J. M. (2019). “Supervised learning with quantum-enhanced feature spaces,” Nature, 567(7747), 209-212. This paper introduces the concept of quantum feature spaces applied to machine learning, demonstrating the QSVM’s potential.
• Lloyd, S., Mohseni, M., & Rebentrost, P. (2014). “Quantum principal component analysis,” Nature Physics, 10(9), 631-633. This foundational paper presents the QPCA algorithm, outlining its theoretical underpinnings and potential for exponential speedup in data analysis.
• Farhi, E., Goldstone, J., & Gutmann, S. (2014). “A Quantum Approximate Optimization Algorithm.” arXiv:1411.4028. This seminal paper introduces QAOA, detailing its theoretical foundation and potential applications in solving optimization problems.
• Amin, M. H., Andriyash, E., Rolfe, J., Kulchytskyy, B., & Melko, R. (2018). “Quantum Boltzmann Machine.” Physical Review X, 8(2), 021050. This paper discusses the implementation of QBMs and demonstrates their potential for learning probability distributions more efficiently than classical approaches.
• Farhi, E., & Neven, H. (2018). “Classification with Quantum Neural Networks on Near Term Processors.” arXiv:1802.06002. This paper explores the use of quantum circuits with parameterized gates for classification tasks, laying the groundwork for the development of QNNs.