Speaker
Description
Quantum kernels (QKs) provide a promising framework for quantum-enhanced machine learning but suffer from the vanishing similarity phenomenon, also known as kernel concentration. As the number of qubits increases, the variance of kernel values decays exponentially, making accurate estimation prohibitively expensive while simultaneously degrading the generalization capability of the resulting kernel on high-dimensional datasets. We introduce Local Fidelity Quantum Kernels (LFQKs), which mitigate kernel concentration by replacing the global fidelity measurement with a combination of fidelity measurements over local subsystems. By selecting polynomially many local projectors with logarithmic locality, LFQKs mitigate the exponential concentration induced by the global measurement. Assuming uniformly random data, we show that the variance of LFQKs decays only polynomially with the number of qubits.
We validate these theoretical predictions across a range of IQP feature maps, circuit depths and system sizes. In all considered architectures, the variance of standard quantum kernels exhibits the expected exponential decay, whereas LFQKs consistently follow the predicted polynomial scaling. We further evaluate the practical impact on synthetic classification tasks whose dimensionality scales with the number of qubits. LFQKs consistently outperform global QK, with accuracy improvements reaching approximately 30 percentage points and approaching the performance of a classical RBF kernel for highly entangled feature maps at larger system sizes. These results demonstrate that local fidelity measurements can provide an effective strategy to mitigate kernel concentration, enabling kernels to remain informative in regimes where conventional global kernels fail.
| Topic | Quantum kernel methods and their applications |
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