用量子核方法预测一维费米系统密度，精度超经典线性核。
Predicting fermionic densities using a Projected Quantum Kernel method
- 基于量子储池可观测量构建投影量子核，用于回归密度分布。
- 测量时间足够长时，误差随时间呈稳定下降趋势，性能优于经典线性核。
- 适用于量子化学与量子物质中的费米系统建模，适合关注量子机器学习的读者。
我们采用基于投影量子核方法的支持向量回归器，预测量子化学与量子物质中一维费米系统密度结构。该核基于可由相互作用里德堡原子实现的量子储池可观测量构建。费米系统训练与测试数据通过密度泛函理论生成。我们在多个哈密顿量参数下测试该方法性能，发现误差随测量时间呈现普遍共性规律。在足够长的测量时间内，该方法性能优于经典线性核，并可与径向基函数核方法媲美。
原文摘要 · Abstract (English)
We use a support vector regressor based on a projected quantum kernel method to predict the density structure of 1D fermionic systems of interest in quantum chemistry and quantum matter. The kernel is built on with the observables of a quantum reservoir implementable with interacting Rydberg atoms. Training and test data of the fermionic system are generated using a Density Functional Theory approach. We test the performance of the method for several Hamiltonian parameters, finding a general common behavior of the error as a function of measurement time. At sufficiently large measurement times, we find that the method outperforms the classical linear kernel method and can be competitive with the radial basis function method.
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