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An introduction to quantum machine learning
M. Schuld, I. Sinayskiy, F. Petruccione
TL;DR
Quantum machine learning asks whether quantum computing can improve classical machine-learning methods, a question motivated by growing data and the absence of a comprehensive theory of quantum learning. The paper systematically surveys approaches across standard classification and clustering methods, finding two dominant strategies: quantum speedups for computational subroutines and reformulations using quantum theory. It concludes that the field remains incomplete, especially regarding the actual learning process and convincing quantum neural-network models.
Problem
Growing data motivates improved machine-learning methods, while a comprehensive theory of quantum learning is still absent.
Method
The paper systematically surveys quantum approaches across standard machine-learning methods, focusing on pattern classification and related clustering tasks.
Results
The review identifies two main approaches: replacing classical algorithms with quantum algorithms for complexity improvements, or reformulating probabilistic methods using quantum theory.
Takeaways & Limitations
Quantum machine learning currently offers promising approaches for speeding distance calculations and connecting probabilistic learning with quantum descriptions, but its broader theory remains open.
Takeaways & Limitations
The review is not complete because it focuses on supervised and unsupervised pattern-classification and clustering methods, excluding reinforcement learning.
Abstract
from arXiv · showhide
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT industry. In the last couple of years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. Ideas range from running computationally costly algorithms or their subroutines efficiently on a quantum computer to the translation of stochastic methods into the language of quantum theory. This contribution gives a systematic overview of the emerging field of quantum machine learning. It presents the approaches as well as technical details in an accessable way, and discusses the potential of a future theory of quantum learning.
1 Introduction
Machine learning derives patterns from data to interpret unknown inputs, while quantum machine learning explores whether quantum computing can improve these methods. The paper introduces this emerging field through classical methods and quantum-information approaches, highlighting both promising directions and unresolved theory.
- Motivation: Machine learning derives patterns from data to interpret previously unknown inputs in tasks including recognition, pattern identification, and strategy optimisation.Applications include search, spam filtering, iris recognition, consumer-behaviour evaluation, financial-risk assessment, and computer-game strategies.
- Motivation: 20% annual growth in globally stored data increases pressure for innovative machine-learning approaches capable of handling big data efficiently.Stored data is described as currently reaching several hundred exabytes.
- Quantum approaches: Quantum machine learning investigates improving classical algorithms by running costly algorithms or subroutines on quantum computers and translating stochastic methods into quantum-theory formalisms.The paper also frames quantum computing through qubit superposition while noting that quantum mechanics restricts access to stored information.
- Open challenges: A comprehensive theory of quantum learning remains only in its first stages, and future work must address how quantum information processing improves the actual learning component.The introduction presents this as an open direction beyond adapting computational subroutines or formalisms.
- Paper scope: The paper surveys quantum approaches to k-nearest neighbours, support vector machines, k-means, neural networks, decision trees, Bayesian theory, and hidden Markov models.Figure 1 groups several approaches around efficient classical-distance calculations, first explorations of quantum models, and reformulation through open quantum systems.
2 Classical and quantum learning
Classical learning derives input-output relations or strategies from data, while quantum machine learning adapts quantum computation to machine-learning problems. The paper highlights both potential efficiency gains and unresolved foundations for a general theory of quantum learning.
- Classical learning: Machine learning derives input-output relations from training data to interpret new inputs, including pattern classification, clustering, and strategy optimisation.
- Classical learning: Supervised learning infers mappings from correct input-output examples, with pattern classification assigning input vectors to predefined classes.
- Classical learning: Unsupervised learning finds patterns without prior examples, especially by clustering data into subgroups without targeting new inputs.
- Classical learning: Reinforcement learning adapts an agent’s strategy through rewards and punishments, but the paper excludes it from its main focus.
- Quantum learning: Quantum machine learning adapts classical algorithms or costly subroutines to quantum computers, using quantum gates, probabilistic measurement, and superposition.
- Quantum learning: A comprehensive theory of quantum learning is absent, with open questions concerning optimisation, quantum distance metrics, decision strategies, and general speedups.
- Quantum learning: Genuinely quantum representations and information-extraction methods may be vital for developing quantum machine learning beyond classical data-encoding ideas.
3 Quantum versions of machine learning algorithms
The section surveys quantum counterparts of standard machine-learning methods, covering classification, clustering, neural networks, decision trees, and hidden Markov models. These approaches use quantum representations, distance or similarity estimation, optimisation, and open-system dynamics, but several methods remain incomplete or unproven.
- Classical learning tasks: Pattern classification is formulated as assigning a new feature vector to a class using labelled training examples.Related tasks include clustering, which assigns similar inputs to shared groups without targeting new inputs.
- Quantum versions of k-nearest neighbour methods: k-nearest neighbour methods classify inputs by nearby vectors, while nearest-centroid methods use preprocessed class means and k = 1.Quantum proposals evaluate similarities or distances through routines such as swap tests, amplitude estimation, and minimum-finding.
- Quantum computing for support vector machines: Quantum support vector machines target the kernel calculations underlying maximum-margin hyperplane optimisation.The kernel matrix contains inner products of feature vectors, making its calculation a relevant quantum-computing target.
- Quantum algorithms for clustering: Quantum k-means clustering alternates nearest-centroid assignments with centroid recalculation, with one proposal based on adiabatic quantum computing.Classical k-means can converge to local minima and depends on initial centroids and the chosen number of clusters.
- Searching for a quantum neural network model: Quantum neural-network proposals include quantum-dot simulations, fuzzy multi-state neurons, and adiabatic implementations, but no known proposal provides a fully functioning efficient quantum pattern-classification method.Translating nonlinear activation functions into a meaningful quantum-mechanical framework remains an open challenge.
- Hidden quantum Markov models: Hidden quantum Markov models represent states with density matrices and transitions with completely positive trace-nonincreasing superoperators, generalising classical models with richer dynamics.Their rigorous treatment and demonstrated ability to solve the problems targeted by classical models remain outstanding.
4 Conclusion
Quantum machine learning research has mainly explored replacing classical machine-learning algorithms with quantum algorithms or expressing stochastic methods through quantum theory. A comprehensive theory of quantum learning remains undeveloped, particularly for simulating the learning process and parameter optimisation.
- 4 Conclusion: Two main approaches dominate quantum machine learning: quantum algorithms replacing classical methods, and quantum descriptions of stochastic processes.The first approach targets complexity improvements, while the second generalises models or supports quantum information tasks.
- 4 Conclusion: Quantum computation primarily accelerates expensive distance calculations in nearest-neighbour, kernel, and clustering methods.The conclusion identifies these methods as the main examples where quantum computation speeds up costly subroutines.
- 4 Conclusion: A comprehensive quantum theory of learning remains at an early stage of development.Only very few contributions address how the learning process itself can be simulated in quantum systems.
- 4 Conclusion: Parameter-optimisation learning methods have not yet been accessed from a quantum perspective.The paper highlights adapting unitary transformations as one challenge for future quantum learning research.