Kernel

In general, kernel methods map data with complex, nonlinear relati­onships into a high-dimen­sio­nal space to make the learning problem easier for further proces­sing with Machine Learning (ML) methods such as the Support Vector Machine (SVM). In Quantum Machine Learning(QML), input data are proces­sed by encoding them into quantum states and thus embed them into the exponen­ti­ally growing quantum Hilbert space. Due to this analogy, it can be formally shown that Quantum Kernel Methods (QKM) can be formu­la­ted as a classi­cal kernel method (e.g., SVM) whose kernel is compu­ted using a quantum compu­ter. Since quantum compu­ta­ti­ons inher­ently feature quantum mecha­ni­cal pheno­mena (such as super­po­si­tion and entan­gle­ment), the resul­ting quantum kernels hold the prospect of desig­ning ML models that can learn complex problems that are out of reach for conven­tio­nal ML methods.