quantum approximate walk algorithm

The encoding of classical to quantum data mapping through trigonometric functions within arithmetic-based quantum computation algorithms leads to the exploitation of multivariate distribution.

The studied variational quantum gate learning mechanism, which relies on agnostic gradient optimization, does not offer algorithmic guarantees for the correlation of results beyond the measured bitstring outputs. Consequently, existing methodologies are inapplicable to this problem.

In this study, we present a classical data-traceable quantum oracle characterized by a circuit depth that increases linearly with the number of qubits. This configuration facilitates the learning of approximate result  patterns through a distributable gate layout.

Moreover, our approach demonstrates that classical preprocessing of mid-quantum measurement data enhances the interpretability of quantum approximate optimization algorithm (QAOA) outputs without requiring full quantum state tomography.

By establishing a traceable mapping between classical input parameters and quantum circuit outcomes, we obtained experimental results on state-of-the-art IBM Pittsburgh hardware that yielded polynomial-time verification of solution quality, primarily because of the efficiency conferred by the shallow quantum oracle.

This hybrid framework bridges the gap between near-term quantum capabilities and practical optimization requirements, offering a pathway toward reliable quantum-classical algorithms for industrial applications.