Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient feature map and careful regularization of the Gram matrix, we demonstrate that the variance information of the resulting quantum Gaussian process can be preserved. We also show that quantum Gaussian processes can be used as a surrogate model for Bayesian optimization, a task that critically relies on the variance of the surrogate model. To demonstrate the performance of this quantum Bayesian optimization algorithm, we apply it to the hyperparameter optimization of a machine learning model which performs regression on a real-world dataset. We benchmark the quantum Bayesian optimization against its classical counterpart and show that quantum version can match its performance.

翻译：高斯过程回归是一种成熟的贝叶斯机器学习方法。我们提出了一种基于参数化量子电路的量子核高斯过程回归新方法。通过采用硬件高效的特征映射以及对格拉姆矩阵进行谨慎的正则化处理，我们证明了所得量子高斯过程的方差信息可以得到保留。我们还表明，量子高斯过程可作为贝叶斯优化的代理模型，而这一任务的关键恰恰依赖于代理模型的方差信息。为验证该量子贝叶斯优化算法的性能，我们将其应用于一个对真实世界数据集进行回归的机器学习模型的超参数优化。我们将量子贝叶斯优化与其经典版本进行基准对比，结果显示量子版本可达到与经典版本相当的性能。