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Quantum kernel methods have been actively examined from both theoretical andpractical perspectives due to the potential of quantum advantage in machinelearning tasks. Despite a provable advantage of fine-tuned quantum kernels forspecific problems, widespread practical usage of quantum kernel methodsrequires resolving the so-called vanishing similarity issue, whereexponentially vanishing variance of the quantum kernels causes implementationinfeasibility and trainability problems. In this work, we analytically andnumerically investigate the vanishing similarity issue in projected quantumkernels with alternating layered ansatzes. We find that variance depends oncircuit depth, size of local unitary blocks and initial state, indicating theissue is avoidable if shallow alternating layered ansatzes are used and initialstate is not highly entangled. Our work provides some insights into designprinciples of projected quantum kernels and implies the need for caution whenusing highly entangled states as input to quantum kernel-based learning models.

Effect of alternating layered ansatzes on trainability of projected quantum kernel