Demonstration of Topological Data Analysis on a Quantum Processor

Abstract

Topological data analysis offers a robust way to extract useful information from noisy, unstructured data by identifying its underlying structure. Recently, an efficient quantum algorithm was proposed [Lloyd, Garnerone, Zanardi, Nat. Commun. 7, 10138 (2016)] for calculating Betti numbers of data points -- topological features that count the number of topological holes of various dimensions in a scatterplot. Here, we implement a proof-of-principle demonstration of this quantum algorithm by employing a six-photon quantum processor to successfully analyze the topological features of Betti numbers of a network including three data points, providing new insights into data analysis in the era of quantum computing.

Typos and minor corrections. For the first time, we have experimentally demonstrated that quantum computing can analyze big data using techniques from topology. Any comments are welcome

References in corpus (9)

• Quantum algorithm for solving linear systems of equations
• Entanglement detection
• Quantum random access memory
• Experimental ten-photon entanglement
• Experimental demonstration of Shor's algorithm with quantum entanglement
• Demonstration of Shor's quantum factoring algorithm using photonic qubits
• Direct generation of three-photon polarization entanglement
• Experimental Blind Quantum Computing for a Classical Client
• Computing the Top Betti Numbers of Semi-algebraic Sets Defined by Quadratic Inequalities in Polynomial Time

Cited by in corpus (20)

• Strong quantum computational advantage using a superconducting quantum processor
• Superconducting Quantum Computing: A Review
• Realization of an Error-Correcting Surface Code with Superconducting Qubits
• Hybrid Quantum-Classical Convolutional Neural Networks
• Experimental Quantum Generative Adversarial Networks for Image Generation
• Quantum-Inspired Support Vector Machine
• Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
• General-purpose quantum circuit simulator with Projected Entangled-Pair States and the quantum supremacy frontier
• Towards quantum advantage via topological data analysis
• Quantum algorithm for persistent Betti numbers and topological data analysis
• Topological data analysis and machine learning
• Finding self-similar behavior in quantum many-body dynamics via persistent homology
• Complexity-Theoretic Limitations on Quantum Algorithms for Topological Data Analysis
• Noise-Resistant Quantum State Compression Readout
• Experimental Quantum Learning of a Spectral Decomposition
• Spin-orbit implementation of Solovay-Kitaev decomposition of single-qubit channels
• Parameter-Parallel Distributed Variational Quantum Algorithm
• Complement Grover's Search Algorithm: An Amplitude Suppression Implementation
• Optimal quantum resource generation in coupled transmons immersed in Markovian baths
• Quantum Recurrence Plot Algorithm Based on Quantum Principal Component Analysis