# Experimental quantum kernel trick with nuclear spins in a solid

@article{Kusumoto2019ExperimentalQK, title={Experimental quantum kernel trick with nuclear spins in a solid}, author={Takeru Kusumoto and Kosuke Mitarai and Keisuke Fujii and Masahiro Kitagawa and Makoto Negoro}, journal={npj Quantum Information}, year={2019}, volume={7}, pages={1-7} }

The kernel trick allows us to employ high-dimensional feature space for a machine learning task without explicitly storing features. Recently, the idea of utilizing quantum systems for computing kernel functions using interference has been demonstrated experimentally. However, the dimension of feature spaces in those experiments have been smaller than the number of data, which makes them lose their computational advantage over explicit method. Here we show the first experimental demonstration…

## 23 Citations

### Machine learning of high dimensional data on a noisy quantum processor

- Computer Sciencenpj Quantum Information
- 2021

A circuit ansatz is constructed that preserves kernel magnitudes that typically otherwise vanish due to an exponentially growing Hilbert space, and error mitigation specific to the task of computing quantum kernels on near-term hardware is implemented.

### Large-scale quantum machine learning

- Computer ScienceArXiv
- 2021

This work measures quantum kernels using randomized measurements to gain a quadratic speedup in computation time and quickly process large datasets and efficiently encode high-dimensional data into quantum computers with the number of features scaling linearly with the circuit depth.

### Quantum machine learning of large datasets using randomized measurements

- Computer ScienceMachine Learning: Science and Technology
- 2023

This work efficiently encode high-dimensional data into quantum computers with the number of features scaling linearly with the circuit depth with a robust approach to noise via a cost-free error mitigation scheme.

### Training Quantum Embedding Kernels on Near-Term Quantum Computers

- PhysicsPhysical Review A
- 2022

This paper presents a meta-analyses of the response of the Higgs boson to the proton-proton collision in a discrete-time environment and shows good support for the theory of quantum entanglement.

### Noisy quantum kernel machines

- Computer SciencePhysical Review A
- 2022

It is shown that decoherence and dissipation can be seen as an implicit regularization for the quantum kernel machines and an upper bound on the generalization error of the model that involves the average purity of the encoded states is derived.

### Quantum AI simulator using a hybrid CPU-FPGA approach

- Computer Science
- 2022

This work focuses on quantum kernels empirically designed for image classification and demonstrates a field programmable gate arrays (FPGA) implementation, and shows that the quantum kernel estimation by the heterogeneous CPU–FPGA computing is 470 times faster than that by a conventional CPU implementation.

### Quantum machine learning beyond kernel methods

- Computer ScienceArXiv
- 2021

It is proved that linear quantum models must utilize exponentially more qubits than data re-uploading models in order to solve certain learning tasks, while kernel methods additionally require exponentially more data points.

### A rigorous and robust quantum speed-up in supervised machine learning

- Computer ScienceNature Physics
- 2021

A rigorous quantum speed-up for supervised classification using a quantum learning algorithm that only requires classical access to data and achieves high accuracy, robust against additive errors in the kernel entries that arise from finite sampling statistics.

### On exploring practical potentials of quantum auto-encoder with advantages

- Computer Science, PhysicsArXiv
- 2021

This work proves that QAE can be used to efficiently calculate the eigenvalues and prepare the corresponding eigenvectors of a high-dimensional quantum state with the low-rank property and proves that the error bounds of the proposed QAE-based methods outperform those in previous literature.

### Towards understanding the power of quantum kernels in the NISQ era

- Computer Science, PhysicsQuantum
- 2021

This work proves that the advantage of quantum kernels is vanished for large size of datasets, few number of measurements, and large system noise and provides theoretical guidance of exploring advanced quantum kernels to attain quantum advantages on NISQ devices.

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