Quantum Kernel Concentration Analysis Mitigation

Quantum Kernel Concentration Analysis Mitigation Understand the issue of kernel matrix concentration in high dimensions and potential mitigation strategies. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

Github Supanut Thanasilp Exponential Concentration In Quantum Kernel We investigated two practical strategies to mitigate exponential concentration in fidelity based quantum kernels: local (patch wise) constructions that aggregate subsystem similarities and multi scale mixtures that combine kernels across patch granularities. Goal: build and evaluate quantum kernels for svms and test whether local (patch wise) and multi scale kernels mitigate exponential concentration as qubit count (dimension d) and or depth increase. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. for each source, an associated concentration bound of quantum kernels is analytically derived. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

Quantum Kernel Quantumexplainer We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. for each source, an associated concentration bound of quantum kernels is analytically derived. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods. In this work, we investigate the effects of hyperparameter choice on the model performance and the generalization gap between classical and quantum kernels. the importance of hyperparameters is well known also for classical machine learning. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. for each source, an associated concentration bound of quantum kernels is analytically derived. We present an empirical study of two mitigation strategies implemented in qiskit: (i) local (patch wise) kernels that aggregate subsystem similarities, and (ii) multi scale kernels that mix local and global similarity across patch granularities. Recent advances focus on tailored circuit designs, noise mitigation strategies, and projective kernels that overcome exponential concentration challenges.