# Supervised learning with quantum enhanced feature spaces

arXiv: https://arxiv.org/abs/1804.11326 · HTML: https://mlsanity.com/paper/1804.11326/

## Key facts

- Cited by 665 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2018.

## Built on by (most cited first, 30 of 665)

- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits](https://mlsanity.com/paper/2107.10845/) (2021)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Noisy intermediate-scale quantum (NISQ) algorithms](https://mlsanity.com/paper/2101.08448/) (2021)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [Exploiting symmetry in variational quantum machine learning](https://mlsanity.com/paper/2205.06217/) (2022)
- [QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer](https://mlsanity.com/paper/2102.12846/) (2021)
- [Theory for Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.08566/) (2022)
- [The Dawn of Quantum Natural Language Processing](https://mlsanity.com/paper/2110.06510/) (2021)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [Quantum machine learning for image classification](https://mlsanity.com/paper/2304.09224/) (2023)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [Quantum federated learning through blind quantum computing](https://mlsanity.com/paper/2103.08403/) (2021)
- [lambeq: An Efficient High-Level Python Library for Quantum NLP](https://mlsanity.com/paper/2110.04236/) (2021)
- [Towards understanding the power of quantum kernels in the NISQ era](https://mlsanity.com/paper/2103.16774/) (2021)
- [Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits](https://mlsanity.com/paper/2203.09376/) (2022)
- [Quantum Self-Attention Neural Networks for Text Classification](https://mlsanity.com/paper/2205.05625/) (2022)
- [Enhancing Generative Models via Quantum Correlations](https://mlsanity.com/paper/2101.08354/) (2021)
- [Representation Learning via Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2111.04225/) (2021)

## Abstract (arXiv)

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.