Quantum speed-up for unsupervised learning

Abstract

We show how the quantum paradigm can be used to speed up unsupervised learning algorithms. More precisely, we explain how it is possible to accelerate learning algorithms by quantizing some of their subroutines. Quantization refers to the process that partially or totally converts a classical algorithm to its quantum counterpart in order to improve performance. In particular, we give quantized versions of clustering via minimum spanning tree, divisive clustering and k-medians that are faster than their classical analogues. We also describe a distributed version of k-medians that allows the participants to save on the global communication cost of the protocol compared to the classical version. Finally, we design quantum algorithms for the construction of a neighbourhood graph, outlier detection as well as smart initialization of the cluster centres.

Entanglement-Based Machine Learning on a Quantum Computer

“…Consider the task of assigning N-dimensional vectors to one of k clusters, each with M representative samples; a quantum computer takes time O½logðMNÞ. The exponential speed-up of the quantum machine learning algorithm, and its potential wide applications, may make it one of the promising applications of quantum computers [2][3][4], in addition to Shor's factoring algorithm [5][6][7][8][9], quantum simulation [10][11][12][13][14], and the quantum algorithm for solving linear equation systems [15,16].In this Letter, we report proof-of-principle demonstrations of the supervised and unsupervised quantum machine learning algorithm [2] on a small-scale photonic quantum processor. The core mathematical task is to assign two-, four-, and eight-dimensional vectors (N ¼ 2; 4; 8) to two different clusters with one reference vector (M ¼ 1) in each cluster.…”

Enhanced Quantum Synchronization via Quantum Machine Learning

“…[38][39][40][41][42][43] In this field, arise a new paradigm concerning the nature of the machine learning components, namely, the agent and the environment. [44] Four categories related to the nature of the learning components can be identified in this two-party system: classicalclassical (CC), classical-quantum (CQ), quantum-classical (QC), and quantum-quantum (QQ). The first of them is related to the classical machine learning.…”

“…In this case, the quantum algorithms which overtake the performance of their classical counterpart have already been shown in supervised and unsupervised machine learning. [44][45][46][47][48][49][50] The last category corresponds to the case in which quantum systems comprise both agent and environment. In such a case, the definition of learning has not been explicitly defined and has to be interpr as the optimization of certain figure of merit.…”

Guest Column

“…Focusing on specific learning problems where quantum algorithms may help, Aïmeur et al [ABG06,ABG13] showed quantum speed-up in learning contexts such as clustering via minimum spanning tree, divisive clustering, and k-medians, using variants of Grover's search algorithm [Gro96]. In the last few years there has been a flurry of interesting results applying various quantum algorithms (Grover's algorithm, but also phase estimation, amplitude amplification [BHMT02], and the HHL algorithm for solving well-behaved systems of linear equations [HHL09]) to specific machine learning problems.…”