Quantum Embedding Search for Quantum Machine Learning

This paper introduces an automated search algorithm (QES, pronounced as “quest”), which derives optimal design of entangling layout for supervised quantum machine learning. First, we establish the connection between the structures of entanglement using CNOT gates and the representations of directed multi-graphs, enabling a well-defined search space. The proposed encoding scheme of quantum entanglement as genotype vectors bridges the ansatz optimization and classical machine learning, allowing efficient search on any well-defined search space. Second, we instigate the entanglement level to reduce the cardinality of the search space to a feasible size for practical implementations. Finally, we mitigate the cost of evaluating the true loss function by using surrogate models via sequential model-based optimization. We demonstrate the feasibility of our proposed approach on simulated and bench-marking datasets, including Iris, Wine and Breast Cancer datasets, which empirically shows that found quantum embedding architecture by QES outperforms manual designs in term of the predictive performance.