Quantum Machine Learning in Feature Hilbert Spaces.
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Summary
This Letter interprets the process of encoding inputs in a quantum state as a nonlinear feature map that maps data to quantum Hilbert space and shows how it opens up a new avenue for the design of quantum machine learning algorithms.
- Type
- article
- Published
- 2018-03-19
- Cited by
- 1,842
- References
- 49
- Access
- Open access
- OpenAlex
- https://openalex.org/W2792946961
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:73432134
Keywords
Hilbert space, Kernel (algebra), Computer science, Quantum computer, Reproducing kernel Hilbert space
References
- Harmonic Analysis on Semigroups
- Quantum support vector machine for big feature and big data classification
- Handbook of Linear Algebra
- The probabilistic mind: prospects for Bayesian cognitive science
- A Shifted Power Method for Homogenous Polynomial Optimization over Unit Spheres
- Quantum Inference on Bayesian Networks
- Reproducing kernel Hilbert spaces in probability and statistics
- Methods in Theoretical Quantum Optics
- Average-case complexity versus approximate simulation of commuting quantum computations
- Searching for quantum speedup in quasistatic quantum annealers
- Gaussian quantum information
- Quantum algorithm for data fitting.
- Encoding a qubit in an oscillator
- Theory of Reproducing Kernels.
- Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
- Universal continuous-variable quantum computation: Requirement of optical nonlinearity for photon counting
- Functions of Positive and Negative Type, and their Connection with the Theory of Integral Equations
- COHERENT STATES: APPLICATIONS IN PHYSICS AND MATHEMATICAL PHYSICS
- The role of the rigged Hilbert space in quantum mechanics
- One clutch or two clutches? Fitness correlates of coexisting alternative female life-histories in the European earwig
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- Continuous-variable quantum neural networks
- Bayesian deep learning on a quantum computer
- Matrix optimization on universal unitary photonic devices
- Quantum optical neural networks
- Expressive power of parametrized quantum circuits
- PennyLane: Automatic differentiation of hybrid quantum-classical computations
- Evaluating analytic gradients on quantum hardware
- Quantum Algorithms for Feedforward Neural Networks
- Potential of quantum computing for drug discovery
- Quantum algorithm and quantum circuit for A-optimal projection: Dimensionality reduction
- Training a Quantum Neural Network to Solve the Contextual Multi-Armed Bandit Problem
- Q Learning with Quantum Neural Networks
- Reinforcement Learning with Deep Quantum Neural Networks
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