Hybrid quantum-classical unsupervised data clustering based on the self-organizing feature map

Abstract

Unsupervised machine learning is one of the main techniques employed in artificial intelligence. We introduce an algorithm for quantum-assisted unsupervised data clustering using the self-organizing feature map, a type of artificial neural network. The complexity of our algorithm scales as O(LN), in comparison to the classical case which scales as O(LMN), where N is the number of samples, M is the number of randomly sampled cluster vectors, and L is the number of the shifts of cluster vectors. We perform a proof-of-concept demonstration of one of the central components on the IBM quantum computer and show that it allows us to reduce the number of calculations in the number of clusters. Our algorithm exhibits exponential decrease in the errors of the distance matrix with the number of runs of the algorithm.

References in corpus (66)

• Quantum Computing in the NISQ era and beyond
• Quantum Machine Learning
• A variational eigenvalue solver on a quantum processor
• Quantum algorithm for solving linear systems of equations
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Machine learning and the physical sciences
• The theory of variational hybrid quantum-classical algorithms
• Quantum support vector machine for big data classification
• A Quantum Approximate Optimization Algorithm
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum Convolutional Neural Networks
• Simulated Quantum Computation of Molecular Energies
• Quantum principal component analysis
• An introduction to quantum machine learning
• Parameterized quantum circuits as machine learning models
• The power of quantum neural networks
• Towards Quantum Chemistry on a Quantum Computer
• Challenges and Opportunities in Quantum Machine Learning
• The quest for a Quantum Neural Network
• Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
• Quantum algorithms for supervised and unsupervised machine learning
• Quantum Data Fitting
• Generalization in quantum machine learning from few training data
• Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor
• Quantum-enhanced machine learning
• Continuous-variable quantum neural networks
• Deep Learning: A Critical Appraisal
• Quantum Approximate Optimization Algorithm for MaxCut: A Fermionic View
• Hybrid Quantum-Classical Convolutional Neural Networks
• Quantum Approximate Optimization of the Long-Range Ising Model with a Trapped-Ion Quantum Simulator
• Reinforcement Learning with Neural Networks for Quantum Feedback
• Quantum speedup for active learning agents
• Quantum Supremacy through the Quantum Approximate Optimization Algorithm
• Quantum Hopfield neural network
• Quantum Machine Learning for Chemistry and Physics
• Optimizing Quantum Error Correction Codes with Reinforcement Learning
• Reachability Deficits in Quantum Approximate Optimization
• Near-optimal quantum circuit for Grover's unstructured search using a transverse field
• Quantum Adversarial Machine Learning
• Quantum autoencoders to denoise quantum data
• Quantum Vision Transformers
• Transformer variational wave functions for frustrated quantum spin systems
• Training A Quantum Optimizer
• Advances in Quantum Reinforcement Learning
• Bayesian Deep Learning on a Quantum Computer
• Transformer Quantum State: A Multi-Purpose Model for Quantum Many-Body Problems
• Quantum Graph Neural Networks
• Generative quantum machine learning via denoising diffusion probabilistic models
• Quantum classification of the MNIST dataset with Slow Feature Analysis
• A quantum k-nearest neighbors algorithm based on the Euclidean distance estimation
• Image classification using quantum inference on the D-Wave 2X
• Quantum Capsule Networks
• A Simple Quantum Neural Net with a Periodic Activation Function
• Sublinear quantum algorithms for training linear and kernel-based classifiers
• Generalized Grover's algorithm for multiple phase inversion states
• Representation of binary classification trees with binary features by quantum circuits
• Alibaba Cloud Quantum Development Platform: Applications to Quantum Algorithm Design
• Deep learning of many-body observables and quantum information scrambling
• Deep recurrent networks predicting the gap evolution in adiabatic quantum computing
• Cancer Detection Using Quantum Neural Networks: A Demonstration on a Quantum Computer
• A Path Towards Quantum Advantage in Training Deep Generative Models with Quantum Annealers
• Compiling Neural Networks for a Computational Memory Accelerator
• Solitonic fixed point attractors in the complex Ginzburg-Landau equation for associative memories
• Quadratic Quantum Speedup for Perceptron Training
• Quantum computing and the brain: quantum nets, dessins d'enfants and neural networks