Quantum algorithms for supervised and unsupervised machine learning

By Seth Lloyd, Masoud Mohseni, Patrick Rebentrost. 2013

897 citations recorded by the source corpus.

Machine-learning tasks frequently involve problems of manipulating and classifying large numbers of vectors in high-dimensional spaces. Classical algorithms for solving such problems typically take time polynomial in the number of vectors and the dimension of the space. Quantum computers are good at manipulating high-dimensional vectors in large tensor product spaces. This paper provides supervised and unsupervised quantum machine learning algorithms for cluster assignment and cluster finding. Quantum machine learning can take time logarithmic in both the number of vectors and their dimension, an exponential speed-up over classical algorithms.

View Paper: https://www.semanticscholar.org/paper/9b0aa51901f05278928bdfcb4e9826a429a81293

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Citations in the corpus

Quantum computing for finance: Overview and prospects (2018, methodology): “While their method also relies on performing a swap test, it boasts an efficiency which is superior to classical algorithms, even when the states’ preparation is taken into account [49].”
Quantum machine learning (2016, unknown): “Returning to the problem of supervised vs. unsupervised learning, Lloyd, Mohseni and Rebentrost [17] discovered quantum machine learning algorithms for cluster assignment and cluster ﬁnding— providing a polynomial speedup over sampling based classical methods for k – means clustering [17, 19].”
Quantum-enhanced machine learning (2016, background): “Exactly this is done in [6, 8], for the purpose of improving computational complexity, with great success, as the improvement can be exponential.”
Quantum Machine Learning for 6G Communication Networks: State-of-the-Art and Vision for the Future (2019, methodology): “For various learning tasks, QML algorithms can provide exponential speed-ups over classical ML algorithms [42], involving large dimensional data, in both supervised and unsupervised learning approaches.”
Quantum Boltzmann Machine (2016, methodology): “Our method is diﬀerent from other existing quantum machine learning proposals [3–13, 15, 16], because quantum mechanics is not only used to facilitate the training process, as in other proposals, but also is exploited in the model.”
An introduction to quantum machine learning (2014, background): “Based on the swap test, Lloyd, Mohseni and Rebentrost [11] recently proposed a way to retrieve the distance between two real-valued n -dimensional vectors (cid:126)a and (cid:126)b through a quantum measurement.”
Quantum convolutional neural network for classical data classification (2021, background): “[8] Seth Lloyd, Masoud Mohseni, and Patrick Rebentrost.”
A quantum-inspired classical algorithm for recommendation systems (2018, background): “Kerenidis and Prakash’s algorithm is one of many QML algorithms [14, 17, 22, 23] that require quantum state preparation assumptions, which state that given an input vectorv , one can quickly form a corresponding quantum state |v⟩.”
Quantum algorithms: an overview (2015, unknown): “These include solving large systems of di(cid:11)erential equations [62, 13], data (cid:12)tting [97] and various tasks in machine learning [65].”
Quantum Recommendation Systems (2016, methodology): “For each user, we split the products into two categories, the “good” and the “bad” recommendations, based on the matrix entries.”
Transformative effects of IoT, Blockchain and Artificial Intelligence on cloud computing: Evolution, vision, trends and open challenges (2019, background): “• Customer churn prediction: Data-driven customer insights are critical to tackle challenge of customer churn prediction [41 , 42] .”