Bandit optimization with quantum kernels: expressiveness and learning

Bayesian optimization with Gaussian processes has been a fundamental tool in machine learning problems where evaluating the objective function is costly. In quantum scenarios, such as NISQ device control or state preparation, quantum kernels promise a unique inductive advantage, but their high dimensionality increases computational complexity and cumulative regret. Recent research proposes projected quantum kernels and classical approximation techniques that reduce the dimensionality of the feature space while preserving the essential properties of the original kernel. This approach enables the design of bandit algorithms with Gaussian processes that operate with approximate kernels, achieving regret bounds that balance approximation error with information gain. The optimal choice of model complexity becomes crucial to maximize sample efficiency without sacrificing expressiveness. In the business realm, the application of these techniques goes beyond quantum; the principles of dimensionality reduction and the balance between expressiveness and learning are directly transferable to problems of AI for businesses that require efficient models with scarce data. For example, in recommendation systems or marketing campaign optimization, where the reward function can be modeled using Gaussian processes with adapted kernels. The integration of custom applications that incorporate these methodologies allows organizations to leverage artificial intelligence robustly and scalably. Furthermore, the use of AWS and Azure cloud services facilitates the deployment of these models in production environments, while business intelligence tools like Power BI convert results into actionable dashboards. Cybersecurity also benefits: AI agents can optimize real-time anomaly detection using bandit techniques. At Q2BSTUDIO, we develop custom software solutions that integrate these advances, from implementing projected quantum kernels to creating complete optimization pipelines. Our business intelligence and process automation services enable companies to capitalize on the expressiveness of models without falling into the curse of dimensionality. Ultimately, the fusion of Gaussian bandit theory with kernel approximation techniques opens the door to more efficient and adaptive applications in quantum and classical environments, and Q2BSTUDIO is ready to guide that transformation.