Establish the classical hardness of the IQP-style feature-map kernel

Establish whether the inner product generated by the IQP-style quantum feature map is classically hard to compute, as required to substantiate the possibility of a quantum advantage for kernels based on that encoding.

Background

The paper includes an IQP-style feature map in its search over quantum-kernel encodings. This construction applies data-dependent single- and two-qubit Pauli-Z interactions between Hadamard layers, and its kernel is based on the resulting state inner products.

The stated motivation for this encoding comes from prior work proposing that the associated inner product may be difficult to compute classically. The computational hardness of that inner product is presented as a conjecture rather than an established result, leaving unresolved whether the encoding can support the claimed possibility of quantum advantage.

References

This embedding was proposed in , where the authors conjecture that the inner product resulting from this encoding is hard to compute classically, suggesting the possibility for a quantum advantage.

— Pareto-optimal quantum kernel selection for unsupervised anomaly detection on real malware beaconing data  (2610.09717 - Micah et al., 7 Oct 2026) in Appendix, Section “Data-encoding feature maps,” subsection “IQP-style feature map”