Kernel of the classicalZitterbewegung

Nuri Ünal

Suzanne Gieser

Seongwook Shin, Ryan Sweke, Hyunseok Jeong

Quantum kernel methods are one of the most explored approaches to quantum machine learning. However, the structural properties and inductive bias of quantum kernels are not fully understood. In this work, we introduce the notion of entangled tensor kernels—a generalization of product kernels from classical kernel theory—and show that all embedding quantum kernels can be understood as an entangled tensor kernel. We discuss how this perspective allows one to gain insights into both the unique inductive bias of quantum kernels and potential methods for their dequantization.

Rainer Kimmich

Grigorii Trofimiuk

A shortening method for large polarization kernels is presented, which results in shortened kernels with the highest error exponent if applied to kernels of size up to 32. It uses lower and upper bounds on partial distances for quick elimination of unsuitable shortening patterns.The proposed algorithm is applied to some kernels of sizes 16 and 32 to obtain shortened kernels of sizes from 9 to 31. These kernels are used in mixed-kernel polar codes of various lengths. Numerical results demonstrate the advantage of polar codes with shortened large kernels compared with shortened and punctured Arikan polar codes, and polar codes with small kernels.