Quantum Fisher kernel for mitigating the vanishing similarity issue

Understand

Quantum kernel method is a machine learning model exploiting quantum computers to calculate the quantum kernels (QKs) that measure the similarity between data.

• Despite the potential quantum advantage of the method, the commonly used fidelity-based QK suffers from a detrimental issue, which we call the vanishing similarity issue; detecting the difference between data becomes hard with the increase of the number of qubits, due to the exponential decrease of the expectation and the variance of the QK.
• This implies the need to design QKs alternative to the fidelity-based one.
• In this work, we propose a new class of QKs called the quantum Fisher kernels (QFKs) that take into account the geometric structure of the data source.