Quantum Gaussian Process Regression for Bayesian Optimization
This work addresses the challenge of implementing Bayesian optimization with quantum computing, though it appears incremental as it matches rather than surpasses classical performance.
The authors tackled the problem of Gaussian process regression by proposing a quantum approach using parameterized quantum circuits, and demonstrated that their quantum Bayesian optimization algorithm can match classical performance on hyperparameter optimization for a real-world regression task.
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.