Quantum fidelity kernel with a trapped-ion simulation platform

Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels becomes an issue. To overcome these challenges, various strategies under the concept of inductive bias have been proposed. Bandwidth optimization is a promising approach that can be implemented using quantum simulation platforms. We propose trapped-ion simulation platforms as a means to compute quantum kernels, filling a gap in the previous literature and demonstrating their effectiveness for binary classification tasks. We compare the performance of the proposed method with an optimized classical kernel and evaluate the robustness of the quantum kernel against noise. The results show that ion trap platforms are well-suited for quantum kernel computation and can achieve high accuracy with only a few qubits.

Figure 1

Decision function (a)–(c) and optimization landscape (d)–(f) of the RBF classical kernel model. (a)–(c) were obtained for the test sets by extracting the optimal hyperparameters of (d)–(f). The three different tasks are referred to as Circles [(a) and (d)], Moons [(b) and (e)], and Ad Hoc [(c) and (f)].

Figure 2

Test accuracy of the quantum kernel model for the Ad Hoc task. The color of each bar corresponds to a given number of qubits and each group of bars corresponds to a set of noise parameters.

Figure 3

Optimization landscape for the quantum kernel model with the validation datasets. The statistical noise strength is given by $s=0.01$ and the depolarizing noise parameter is $p=0.01$. The left column corresponds to $N=2$ while the right column corresponds to $N=6$. The top row is the Circles task, the middle row is the Moons task, and the bottom row is the Ad Hoc task.