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Quantum kernel method is a machine learning model exploiting quantumcomputers to calculate the quantum kernels (QKs) that measure the similaritybetween data. Despite the potential quantum advantage of the method, thecommonly used fidelity-based QK suffers from a detrimental issue, which we callthe vanishing similarity issue; detecting the difference between data becomeshard with the increase of the number of qubits, due to the exponential decreaseof the expectation and the variance of the QK. This implies the need to designQKs alternative to the fidelity-based one. In this work, we propose a new classof QKs called the quantum Fisher kernels (QFKs) that take into account thegeometric structure of the data source. We analytically and numericallydemonstrate that the QFK based on the anti-symmetric logarithmic derivatives(ALDQFK) can avoid the issue when the alternating layered ansatzs (ALAs) areused, while the fidelity-based QK cannot even with the ALAs. Moreover, theFourier analysis numerically elucidates that the ALDQFK can have expressivitycomparable to that of the fidelity-based QK. These results indicate that theQFK paves the way for practical applications of quantum machine learning withpossible quantum advantages.

Quantum Fisher kernel for mitigating the vanishing similarity issue