Supervised learning with quantum enhanced feature spaces

Abstract

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for classification problems. However, there are limitations to the successful solution to such problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element to computational speed-ups afforded by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here, we propose and experimentally implement two novel methods on a superconducting processor. Both methods represent the feature space of a classification problem by a quantum state, taking advantage of the large dimensionality of quantum Hilbert space to obtain an enhanced solution. One method, the quantum variational classifier builds on [1,2] and operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs. In the second, a quantum kernel estimator, we estimate the kernel function and optimize the classifier directly. The two methods present a new class of tools for exploring the applications of noisy intermediate scale quantum computers [3] to machine learning.

Fixed typos, added figures and discussion about quantum error mitigation

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• Quantum Support Vector Machines for Continuum Suppression in B Meson Decays
• Enhancing distributed sensing with imperfect error correction
• Can Noise on Qubits Be Learned in Quantum Neural Network? A Case Study on QuantumFlow
• On Optimizing Hyperparameters for Quantum Neural Networks
• Quantum Circuit Parameters Learning with Gradient Descent Using Backpropagation
• A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method
• Quantum Kernel Machine Learning With Continuous Variables
• Quantum Next-Generation Reservoir Computing and Its Quantum Optical Implementation
• Gradients and frequency profiles of quantum re-uploading models
• Optimize the event selection strategy to study the anomalous quartic gauge couplings at muon colliders using the support vector machine and quantum support vector machine
• Stochastic Approximation of Variational Quantum Imaginary Time Evolution
• Quantum Algorithm For Estimating Eigenvalue
• Practical quantum simulation of small-scale non-Hermitian dynamics
• Parameter-Parallel Distributed Variational Quantum Algorithm
• Information flow in parameterized quantum circuits
• Comparative Analysis of Quantum and Classical Support Vector Classifiers for Software Bug Prediction: An Exploratory Study
• Optimisation-free Classification and Density Estimation with Quantum Circuits
• Quantum neural compressive sensing for ghost imaging
• Quantum computing for genomics: conceptual challenges and practical perspectives
• Realizing a Continuous Set of Two-Qubit Gates Parameterized by an Idle Time
• Implementation and Empirical Evaluation of a Quantum Machine Learning Pipeline for Local Classification
• A simple framework for contrastive learning phases of matter
• Quantum Kernel Evaluation via Hong-Ou-Mandel Interference
• Quantum gradient evaluation through quantum non-demolition measurements
• Assisted quantum simulation of open quantum systems
• Framework for Learning and Control in the Classical and Quantum Domains
• Maximising Quantum-Computing Expressive Power through Randomised Circuits
• Non-Classical Kernels in Continuous Variable Systems
• Quantum Support Vector Machine-Based Classification of GPS Signal Reception Conditions
• Quantum density estimation with density matrices: Application to quantum anomaly detection
• Machine-Learning Insights into the Entanglement-trainability Correlation of Parameterized Quantum Circuits
• Improved resource-tunable near-term quantum algorithms for transition probabilities, with applications in physics and variational quantum linear algebra
• Quantum Computing for Data Centric Engineering and Science
• Quantum Kerr Learning
• Mitigating Quantum Gate Errors for Variational Eigensolvers Using Hardware-Inspired Zero-Noise Extrapolation
• Robust Quantum Reservoir Computing for Molecular Property Prediction
• A quantum extension of SVM-perf for training nonlinear SVMs in almost linear time
• Variational Optimization for Quantum Problems using Deep Generative Networks
• Simple Hamiltonian dynamics is a powerful quantum processing resource
• Harnessing Quantum Support Vector Machines for Cross-Domain Classification of Quantum States
• Using gradient-based algorithms to determine ground state energies on a quantum computer
• Universal noise-precision relations in variational quantum algorithms
• Contextual Quantum Neural Networks for Stock Price Prediction
• Rigorous noise reduction with quantum autoencoders
• Experimental benchmarking of quantum state overlap estimation strategies with photonic systems
• Perturbative readout error mitigation for near term quantum computers
• Entanglement Detection with Quantum-inspired Kernels and SVMs
• Streaming IoT Data and the Quantum Edge: A Classic/Quantum Machine Learning Use Case
• Quantum machine learning for multiclass classification beyond kernel methods
• Quantum Adjoint Convolutional Layers for Effective Data Representation
• Measurement-based quantum computation from Clifford quantum cellular automata
• Quantum locally linear embedding for nonlinear dimensionality reduction
• The Future of Computing: Bits + Neurons + Qubits
• Quantum Extremal Learning
• An Optimized Quantum Maximum or Minimum Searching Algorithm and its Circuits
• Supervised Learning Guarantee for Quantum AdaBoost
• Optimal compilation of parametrised quantum circuits
• Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelity
• Conditions for a quadratic quantum speedup in nonlinear transforms with applications to energy contract pricing
• On the similarity of bandwidth-tuned quantum kernels and classical kernels
• Single entanglement connection architecture between multi-layer bipartite Hardware Efficient Ansatz
• Quantum supremacy with analog quantum processors for material science and machine learning
• Tangible reduction in learning sample complexity with large classical samples and small quantum system
• Learning Fourier series with parametrized quantum circuits
• Engineering non-Markovianity from defect-phonon interactions
• On the role of coherence for quantum computational advantage
• VQE-generated quantum circuit dataset for machine learning
• Estimating many properties of a quantum state via quantum reservoir processing
• Quantum enhanced stratification of Breast Cancer: exploring quantum expressivity for real omics data
• Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach
• QFT based quantum arithmetic logic unit on IBM quantum computer
• Synergic quantum generative machine learning
• Pitfalls when tackling the exponential concentration of parameterized quantum models
• Quantum resources in Harrow-Hassidim-Lloyd algorithm
• Application of Quantum Pre-Processing Filter for Binary Image Classification with Small Samples
• Quantum Local Differential Privacy and Quantum Statistical Query Model
• Towards solving the BCS Hamiltonian gap in Near-Term Quantum Computers
• QKAN: quantum Kolmogorov-Arnold networks with applications in machine learning and multivariate state preparation
• Trained quantum neural networks are Gaussian processes
• Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise
• Measurement-based quantum machine learning
• Almost fault-tolerant quantum machine learning with drastic overhead reduction
• Multidimensional Quantum Generative Modeling by Quantum Hartley Transform
• A Monte Carlo Tree Search approach to QAOA: finding a needle in the haystack
• Implementing High-fidelity Two-Qubit Gates in Superconducting Coupler Architecture with Novel Parameter Regions
• Quantum Technology for Military Applications
• A Survey of Classical And Quantum Sequence Models
• A Unified Framework for Quantum Supervised Learning
• Benchmarking quantum tomography completeness and fidelity with machine learning
• Resource-Efficient Hadamard Test Tailored Variational Framework for Nonlinear Dynamics on Quantum Computers
• Generating Quantum Reservoir State Representations with Random Matrices
• Mitigating exponential concentration in covariant quantum kernels for subspace and real-world data
• Typical Machine Learning Datasets as Low-Depth Quantum Circuits
• An Efficient Gradient Sensitive Alternate Framework for VQE with Variable Ansatz
• Quantum Alphatron: quantum advantage for learning with kernels and noise
• Evolved Quantum Boltzmann Machines
• Supervised binary classification of small-scale digit images and weighted graphs with a trapped-ion quantum processor
• Quantum Kernel Methods: Convergence Theory, Separation Bounds and Applications to Marketing Analytics
• Quantum Curriculum Learning
• Assessing Projected Quantum Kernels for the Classification of IoT Data
• Crosstalk-Based Parameterized Quantum Circuit Approximation
• The Levy-Lieb embedding of density functional theory and its Quantum Kernel: Illustration for the Hubbard Dimer using near-term quantum algorithms
• Next Generation Resilient Cyber-Physical Systems
• Expressivity of deterministic quantum computation with one qubit
• A Cutting-plane Method for Semidefinite Programming with Potential Applications on Noisy Quantum Devices
• Implications of Deep Circuits in Improving Quality of Quantum Question Answering
• Agnostic Process Tomography
• Quantum evolution kernel : Machine learning on graphs with programmable arrays of qubits
• Constant-time Quantum Algorithm for Homology Detection in Closed Curves
• Quantum circuit-like learning: A fast and scalable classical machine-learning algorithm with similar performance to quantum circuit learning
• Quantitative convergence of trained quantum neural networks to a Gaussian process
• Bayesian machine learning for Boltzmann machine in quantum-enhanced feature spaces
• NISQ algorithm for the matrix elements of a generic observable
• Quantum State Preparation for Probability Distributions with Reflection Symmetry Using Matrix Product States
• Variable Hyperparameterized Gaussian Kernel using Displaced Squeezed Vacuum State
• Ground state energy and magnetization curve of a frustrated magnetic system from real-time evolution on a digital quantum processor
• Quadratic speed-ups in quantum kernelized binary classification
• Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learning
• Quantum Computing Methods for Malware Detection
• Qubit Readout Error Mitigation with Bit-flip Averaging
• Composability of global phase invariant distance and its application to approximation error management
• Freedom of mixer rotation-axis improves performance in the quantum approximate optimization algorithm
• Performance of Grover's search algorithm with diagonalizable collective noises
• Quantum neural network autoencoder and classifier applied to an industrial case study
• SQL2Circuits: Estimating Cardinalities, Execution Times, and Costs for SQL Queries with Quantum Natural Language Processing
• Estimation of mutual information via quantum kernel method
• Quantum fidelity kernel with a trapped-ion simulation platform
• Dynamical transition in controllable quantum neural networks with large depth
• Batched Line Search Strategy for Navigating through Barren Plateaus in Quantum Circuit Training
• Compressed sensing enhanced by quantum approximate optimization algorithm
• Expressiveness of Commutative Quantum Circuits: A Probabilistic Approach
• Adaptive Quantum Generative Training using an Unbounded Loss Function
• Empirical Power of Quantum Encoding Methods for Binary Classification
• A Machine Learning Approach to Boost the Vehicle-2-Grid Scheduling
• Learning out-of-time-ordered correlators with classical kernel methods
• Quantum transfer component analysis for domain adaptation
• A coherent approach to quantum-classical optimization
• Quantum-data-driven dynamical transition in quantum learning
• A quantum machine learning classifier to search for new physics
• Generalization Study of Quantum Neural Network
• Integrated Encoding and Quantization to Enhance Quanvolutional Neural Networks
• Universal approximation of continuous functions with minimal quantum circuits
• When Quantum and Classical Models Disagree: Learning Beyond Minimum Norm Least Square
• Ensuring superior learning outcomes and data security for authorized learner
• Double descent in quantum kernel methods
• Classification using a two-qubit quantum chip
• Weighted Approximate Quantum Natural Gradient for Variational Quantum Eigensolver
• Edge of Many-Body Quantum Chaos in Quantum Reservoir Computing
• Self-attention U-Net decoder for toric codes
• Analysis of Quantum Image Representations for Supervised Classification
• Quantum Machine Learning for Identifying Transient Events in X-ray Light Curves
• The Dual Role of Low-Weight Pauli Propagation: A Flawed Simulator but a Powerful Initializer for Variational Quantum Algorithms
• Quantum Enhanced Anomaly Detection for ADS-B Data using Hybrid Deep Learning
• Multi-channel convolutional neural quantum embedding
• Entanglement dynamics and performance of two-qubit gates for superconducting qubits under non-Markovian effects
• Continuous-variable photonic quantum extreme learning machines for fast collider-data selection
• Shot-based quantum encoding: a data-loading paradigm for quantum neural networks
• Harnessing a 256-qubit Neutral Atom Simulator for Graph Classification
• Experimental kernel-based quantum machine learning in finite feature space
• Learning Reduced Representations for Quantum Classifiers
• Benchmarking of quantum fidelity kernels for Gaussian process regression
• Sample-size-reduction of quantum states for the noisy linear problem
• Data science and Machine learning in the Clouds: A Perspective for the Future
• SWAP Test for an Arbitrary Number of Quantum States
• The Holy Grail of Quantum Artificial Intelligence: Major Challenges in Accelerating the Machine Learning Pipeline
• An unsupervised feature learning for quantum-classical convolutional network with applications to fault detection
• Equivalence between exponential concentration in quantum machine learning kernels and barren plateaus in variational algorithms
• Quantum feature-map learning with reduced resource overhead
• The Effect of Noise on the Performance of Variational Algorithms for Quantum Chemistry
• Exploiting biased noise in variational quantum models
• Mean-field limit from general mixtures of experts to quantum neural networks
• Molecular resonance identification in complex absorbing potentials via integrated quantum computing and high-throughput computing
• Auto Quantum Machine Learning for Multisource Classification
• Clustering and enhanced classification using a hybrid quantum autoencoder
• Large Scale Diverse Combinatorial Optimization: ESPN Fantasy Football Player Trades
• Variational Quantum Models for Knowledge Graph Embeddings on NISQ Devices
• Verifying Adversarial Robustness in Quantum Machine Learning: from theory to physical validation via a software tool
• Quantum-Inspired Weight-Constrained Neural Network: Reducing Variable Numbers by 100x Compared to Standard Neural Networks
• Application of Deep Learning to Jet Charge Discrimination
• Quantum Computation
• Kernel Reboot: Breaking the Boundaries of Neural Tangent Kernels for Neural Fields
• A Quantum Variational Approach to Prototypical Recurrent Unit
• Towards quantum machine learning for assessing the resilience of post-quantum cryptography
• Variational Quantum Generative Modeling by Sampling Expectation Values of Tunable Observables
• State transfer with separable optical beams and variational quantum algorithms with classical light
• Accelerating Quantum State Encoding with SIMD: Design, Implementation, and Benchmarking
• Construction of 'Support Vector' Machine Feature Spaces via Deformed Weyl-Heisenberg Algebra
• Quantum Perceptron Revisited: Computational-Statistical Tradeoffs
• Transformer fault diagnosis using an efficient simulation-driven variational quantum classifier with domain-aware feature encoding
• Quantum-classical simulation of quantum field theory by quantum circuit learning
• Optimizing Quantum Variational Circuits with Deep Reinforcement Learning
• Introducing Reduced-Width QNNs, an AI-inspired Ansatz Design Pattern
• Quantum Machine Learning with SQUID
• Quantum Gate Pattern Recognition and Circuit Optimization for Scientific Applications
• Data-driven Quantum Dynamical Embedding Method for Long-term Prediction on Near-term Quantum Computers
• Quantifying the Expressive Capacity of Quantum Systems: Fundamental Limits and Eigentasks
• Implementation of a Hamming-Distance-Like Genomic Quantum Classifier Using Inner Products on IBMQX4 and IBMQX16
• Synthetic weather radar using hybrid quantum-classical machine learning
• Multivariate unbounded quantum regression via log-ratio probabilities mitigating barren plateaus
• Random Graph-Based Neuromorphic Learning with a Layer-Weaken Structure
• Hybrid quantum recurrent neural network for remaining useful life prediction of turbofan engines
• New perspectives on quantum kernels through the lens of entangled tensor kernels
• Interpolation-based coordinate descent method for parameterized quantum circuits
• Training Hybrid Classical-Quantum Classifiers via Stochastic Variational Optimization
• Extended parameter shift rules with minimal derivative variance for parameterized quantum circuits
• K-sparse Pure State Tomography with Phase Estimation
• Noise-Resilient Quantum Reinforcement Learning
• Efficient classical computation of the neural tangent kernel of quantum neural networks
• Superior resilience to poisoning and amenability to unlearning in quantum machine learning
• Quantum generative classification with mixed states
• Quantum Model-Discovery
• Modeling and benchmarking quantum optical neurons for efficient neural computation
• Classical Neural Networks on Quantum Devices via Tensor Network Disentanglers: A Case Study in Image Classification
• Fast suppression of classification error in variational quantum circuits