Quantum machine learning: a classical perspective

Abstract

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets are motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed-up classical machine learning algorithms. Here we review the literature in quantum machine learning and discuss perspectives for a mixed readership of classical machine learning and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in machine learning are identified as promising directions for the field. Practical questions, like how to upload classical data into quantum form, will also be addressed.

v3 33 pages; typos corrected and references added

References in corpus (25)

• Quantum algorithm for solving linear systems of equations
• A Quantum Approximate Optimization Algorithm
• An introduction to quantum machine learning
• Quantum random access memory
• The quest for a Quantum Neural Network
• Quantum autoencoders for efficient compression of quantum data
• Limits on Fundamental Limits to Computation
• Architectures for a quantum random access memory
• Quantum generalisation of feedforward neural networks
• Creating superpositions that correspond to efficiently integrable probability distributions
• A quantum linear system algorithm for dense matrices
• Optimal Quantum Measurements of Expectation Values of Observables
• Quantum Simulations of Classical Annealing Processes
• Tomography and Generative Data Modeling via Quantum Boltzmann Training
• A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem
• Size dependence of the minimum excitation gap in the Quantum Adiabatic Algorithm
• The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
• Quantum Algorithms for Fixed Qubit Architectures
• A statistical model for tensor PCA
• Improved Bounds on Quantum Learning Algorithms
• Preparing thermal states of quantum systems by dimension reduction
• Learning with Errors is easy with quantum samples
• A Survey of Quantum Learning Theory
• On the adiabatic condition and the quantum hitting time of Markov chains
• Quantum Inspired Training for Boltzmann Machines

Cited by in corpus (147)

• Supervised learning with quantum enhanced feature spaces
• Machine learning and the physical sciences
• Noisy intermediate-scale quantum (NISQ) algorithms
• Superconducting Qubits: Current State of Play
• The power of quantum neural networks
• A rigorous and robust quantum speed-up in supervised machine learning
• Quantum Computing for Finance: State of the Art and Future Prospects
• Hierarchical quantum classifiers
• Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
• The prospects of quantum computing in computational molecular biology
• Quantum Hopfield neural network
• Trainability of Dissipative Perceptron-Based Quantum Neural Networks
• Quantum generative adversarial learning in a superconducting quantum circuit
• Opportunities in Quantum Reservoir Computing and Extreme Learning Machines
• Machine learning meets quantum physics
• Variational Quantum Eigensolver with Fewer Qubits
• Quantum machine learning for quantum anomaly detection
• Hybrid quantum convolutional neural networks model for COVID-19 prediction using chest X-Ray images
• Quantum principal component analysis only achieves an exponential speedup because of its state preparation assumptions
• Quantum Adversarial Machine Learning
• Quantum Neuron: an elementary building block for machine learning on quantum computers
• Neutral Atom Quantum Computing Hardware: Performance and End-User Perspective
• Mixed Quantum-Classical Method For Fraud Detection with Quantum Feature Selection
• Temporal Information Processing on Noisy Quantum Computers
• Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning
• Quantum Machine Learning in High Energy Physics
• Approximate amplitude encoding in shallow parameterized quantum circuits and its application to financial market indicator
• Quantum Machine Learning: from physics to software engineering
• Quantum-assisted Helmholtz machines: A quantum-classical deep learning framework for industrial datasets in near-term devices
• A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance
• Universal discriminative quantum neural networks
• QReLU and m-QReLU: Two novel quantum activation functions to aid medical diagnostics
• Modelling Non-Markovian Quantum Processes with Recurrent Neural Networks
• Variational Quantum Singular Value Decomposition
• Hybrid quantum-classical reservoir computing of thermal convection flow
• Classification with Quantum Machine Learning: A Survey
• Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets
• Resilience of quantum random access memory to generic noise
• Efficient Representation of Topologically Ordered States with Restricted Boltzmann Machines
• Quantum linear systems algorithms: a primer
• Quantum Natural Language Processing on Near-Term Quantum Computers
• The theory of the quantum kernel-based binary classifier
• Quantum enhancements for deep reinforcement learning in large spaces
• An improved quantum-inspired algorithm for linear regression
• Variational inference with a quantum computer
• Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials
• Machine learning \& artificial intelligence in the quantum domain
• Imaginary components of out-of-time correlators and information scrambling for navigating the learning landscape of a quantum machine learning model
• Symmetry enhanced variational quantum spin eigensolver
• The Efficient Preparation of Normal Distributions in Quantum Registers
• Quantum semi-supervised generative adversarial network for enhanced data classification
• Predicting toxicity by quantum machine learning
• Optimization and learning of quantum programs
• Convex optimization of programmable quantum computers
• Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data
• Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted
• Generative training of quantum Boltzmann machines with hidden units
• Generative machine learning with tensor networks: benchmarks on near-term quantum computers
• Neural network-based prediction of the secret-key rate of quantum key distribution
• Cost function embedding and dataset encoding for machine learning with parameterized quantum circuits
• Quantum machine learning with adaptive linear optics
• On the Sample Complexity of Quantum Boltzmann Machine Learning
• Hybrid classical-quantum linear solver using Noisy Intermediate-Scale Quantum machines
• Quantum-assisted associative adversarial network: Applying quantum annealing in deep learning
• Machine Learning and Quantum Devices
• Retrieving information from a black hole using quantum machine learning
• Optimal universal learning machines for quantum state discrimination
• Dequantizing quantum machine learning models using tensor networks
• Compact quantum kernel-based binary classifier
• Transition Role of Entangled Data in Quantum Machine Learning
• Approximate complex amplitude encoding algorithm and its application to data classification problems
• Speed-up Quantum Perceptron via Shortcuts to Adiabaticity
• Optimal Usage of Quantum Random Access Memory in Quantum Machine Learning
• End-to-end resource analysis for quantum interior point methods and portfolio optimization
• Approximation of quantum control correction scheme using deep neural networks
• Quantum algorithms for scientific computing
• Software Supply Chain Vulnerabilities Detection in Source Code: Performance Comparison between Traditional and Quantum Machine Learning Algorithms
• Mapping the Landscape of Generative AI in Network Monitoring and Management
• Quantum Bandits
• Effects of quantum resources on the statistical complexity of quantum circuits
• Statistical Complexity of Quantum Learning
• Semisupervised Anomaly Detection using Support Vector Regression with Quantum Kernel
• Quantum Mean Embedding of Probability Distributions
• Supervised learning of few dirty bosons with variable particle number
• Experimental demonstration of quantum learning speed-up with classical input data
• Natural orbitals and sparsity of quantum mutual information
• Entanglement-induced provable and robust quantum learning advantages
• Quantum error reduction with deep neural network applied at the post-processing stage
• Performance analysis of a hybrid agent for quantum-accessible reinforcement learning
• A Continuous Variable Born Machine
• Small quantum computers and large classical data sets
• Continuous Variable Quantum Perceptron
• Quantum-machine-assisted Drug Discovery
• Magnetic Phases of Spatially-Modulated Spin-1 Chains in Rydberg Excitons: Classical and Quantum Simulations
• A quantum algorithm for simulating non-sparse Hamiltonians
• Graph kernels encoding features of all subgraphs by quantum superposition
• Statistical Limits of Supervised Quantum Learning
• Robust quantum classifier with minimal overhead
• Quantum Splines for Non-Linear Approximations
• Quantum Supervised Learning
• Two-level Quantum Walkers on Directed Graphs II: An Application to qRAM
• QRAM: A Survey and Critique
• Binary Classification with Classical Instances and Quantum Labels
• Quantum random access memory with transmon-controlled phonon routing
• Quantum Kernel Evaluation via Hong-Ou-Mandel Interference
• Quantum secure learning with classical samples
• Variational quantum simulation of long-range interacting systems
• Classification and reconstruction for single-pixel imaging with classical and quantum neural networks
• Liouvillian skin effect in quantum neural networks
• Approximating Hamiltonian dynamics with the Nyström method
• Tangible reduction in learning sample complexity with large classical samples and small quantum system
• A quantum random access memory (QRAM) using a polynomial encoding of binary strings
• Contextual Quantum Neural Networks for Stock Price Prediction
• Efficient Gaussian State Preparation in Quantum Circuits
• Synergic quantum generative machine learning
• Unitary Evolutions Sourced By Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories
• Basic quantum subroutines: finding multiple marked elements and summing numbers
• Quantum and Classical Algorithms for Approximate Submodular Function Minimization
• $Classi|Q⟩$ Towards a Translation Framework To Bridge The Classical-Quantum Programming Gap
• Polynomial T-depth Quantum Solvability of Noisy Binary Linear Problem: From Quantum-Sample Preparation to Main Computation
• Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise
• An Amplitude-Based Implementation of the Unit Step Function on a Quantum Computer
• Implications of Deep Circuits in Improving Quality of Quantum Question Answering
• Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learning
• Quantum Alphatron: quantum advantage for learning with kernels and noise
• Analogy between Boltzmann machines and Feynman path integrals
• Quantum Deformed Neural Networks
• Unified Architecture for Quantum Lookup Tables
• Experimental kernel-based quantum machine learning in finite feature space
• Variational simulation of higher-spin systems on qubit-based quantum simulators
• More Practical and Adaptive Algorithms for Online Quantum State Learning
• Machine Learning Kernel Method from a Quantum Generative Model
• Quantum Machine Learning For Classical Data
• Ensuring superior learning outcomes and data security for authorized learner
• SWAP Test for an Arbitrary Number of Quantum States
• Learning to Utilize Correlated Auxiliary Noise: A Possible Quantum Advantage
• Multi-Armed Bandits and Quantum Channel Oracles
• Quantum-Inspired Computing: Can it be a Microscopic Computing Model of the Brain?
• Neural network ensemble for computing cross sections for rotational transitions in H${}_2$O + H${}_2$O collisions
• Information-Theoretic Limits of Quantum Learning via Data Compression
• Quantum Data Structure for Range Minimum Query
• High-expressibility Quantum Neural Networks using only classical resources
• A Forecasting System of Computational Time of DFT/TDDFT Calculations under the Multiverse ansatz via Machine Learning and Cheminformatics
• Comment on arXiv:2307.08384 "Efficient Quantum State Preparation with Walsh Series"
• Enhanced local addressability of a spin array with local exchange pulses and global microwave driving
• Quantum Perceptron Revisited: Computational-Statistical Tradeoffs
• Quantum-Inspired Weight-Constrained Neural Network: Reducing Variable Numbers by 100x Compared to Standard Neural Networks