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tags: experiment, quantum kernel estimation, quantum computing, 2021
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# [[WIP]Machine learning of high dimensional data on a noisy quantum processor](https://arxiv.org/abs/2101.09581)
Evan Peters, João Caldeira, Alan Ho, Stefan Leichenauer, Masoud Mohseni, Hartmut Neven, Panagiotis Spentzouris, Doug Strain, Gabriel N. Perdue

## Abstract
We present a quantum kernel method for high-dimensional data analysis using Google's universal quantum processor, Sycamore. This method is successfully applied to the cosmological benchmark of supernova classification using real spectral features with no dimensionality reduction and without vanishing kernel elements. Instead of using a synthetic dataset of low dimension or pre-processing the data with a classical machine learning algorithm to reduce the data dimension, this experiment demonstrates that machine learning with real, high dimensional data is possible using a quantum processor; but it requires careful attention to shot statistics and mean kernel element size when constructing a circuit ansatz. Our experiment utilizes 17 qubits to classify 67 dimensional data - significantly higher dimensionality than the largest prior quantum kernel experiments - resulting in classification accuracy that is competitive with noiseless simulation and comparable classical techniques.

## Backgrounds
超新星爆発の種類をスペクトルから教師あり分類
それを既存のGoogleの量子コンピュータでやったまで。
特徴は
- qubitのサイズが大きくても結果がよかったこと。
- “natural” datasetsに対しては今のデバイスでうまくいった

## Methods
要するに実機での実験

回路設計で、統計誤差を減らすことに成功!?

## Open Problems

> While the circuits we implemented are not candidates for demonstrating quantum advantage, these findings suggest quantum kernel methods may be capable of achieving high classification accuracy on near-term devices.

Quantum Advantageは示していない。

> Careful attention must be paid to the impact of shot statistics and kernel element magnitudes when evaluating the performance of quantum kernel methods. This work highlights the need for further theoretical investigation under these constraints, as well as motivates further studies in the properties of noisy kernels.

有限shot数による推定誤差が問題になる。

> The main open problem is to identify a “natural” dataset that could lead to beyond-classical performance for quantum machine learning.

古典処理では難しそうな"natural" dataset探しが課題になる。
例えば、
- quantum data from simulations of quantum many-body systems near a critical point (Quantum advantage for differential equation analysis (2020), rXiv:2010.15776)
- solving linear and nonlinear systems of equations on a quantum computer ( Quantum algorithm for nonlinear differential equations (2020), arXiv:2011.06571)

> Very recently, a quantum advantage has been proposed for some engineered dataset and numerically validated on up to 30 qubits in TFQ using similar quantum kernel methods as described in this experimental demonstration

これは[Power of data in quantum machine learning](https://arxiv.org/abs/2011.01938)のことを指している。