Quantum Approximate Walk Algorithm

TL;DR

This paper introduces a shallow quantum circuit-based approach for approximate optimization, improving interpretability and verifiability of quantum algorithms on near-term hardware, with demonstrated experimental results.

Contribution

It presents a classical data-traceable quantum oracle with linear circuit depth and enhances QAOA interpretability through classical preprocessing, bridging quantum hardware limitations and practical optimization.

Findings

Successful implementation on IBM Pittsburgh hardware

Polynomial-time verification of solution quality

Enhanced interpretability of quantum outputs

Abstract

The encoding of classical to quantum data mapping through trigonometric functions within arithmetic-based quantum computation algorithms leads to the exploitation of multivariate distributions. 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 shallow quantum circuit (SQC) layout. Moreover, our approach demonstrates that the 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 an inferable mapping between the classical input and quantum circuit outcomes, we obtained experimental results on the state-of-the-art IBM Pittsburgh hardware, which yielded polynomial-time verification of the solution quality. 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.