Mohammad Aamir Sohail

Mohammad Aamir Sohail, Mohsen Heidari, S. Sandeep Pradhan

Variational quantum algorithms, optimized using gradient-based methods, often exhibit sub-optimal convergence performance due to their dependence on Euclidean geometry. Quantum natural gradient descent (QNGD) is a more efficient method that incorporates the geometry of the state space via a quantum information metric. However, QNGD is computationally intensive and suffers from high sample complexity. In this work, we formulate a novel quantum information metric and construct an unbiased estimator for this metric using single-shot measurements. We develop a quantum optimization algorithm that leverages the geometry of the state space via this estimator while avoiding full-state tomography, as in conventional techniques. We provide the convergence analysis of the algorithm under mild conditions. Furthermore, we provide experimental results that demonstrate the better sample complexity and faster convergence of our algorithm compared to the state-of-the-art approaches. Our results illustrate the algorithm's ability to avoid saddle points and local minima.

Mohammad Aamir Sohail, Gabriela Pinheiro, Yasemin Poyraz Kocak et al.

Edge detection refers to identifying points in a digital image where intensity changes sharply, indicating object boundaries or structural features. Corners are locations where gray-level intensity changes abruptly in multiple directions and are widely used in feature extraction, object tracking, and 3D modeling. In this study, we present a quantum implementation of Sobel-based edge detection and Harris-style corner detection. Two quantum image encoding methods - Flexible Representation of Quantum Images (FRQI) and Quantum Probability Image Encoding (QPIE) - are used to encode the input data and are comparatively analyzed. The proposed approach introduces a quantum gradient computation scheme based on lag-2 differences, enabling the evaluation of gradient-like features in superposition. To improve detection quality and reduce false positives, a classical post-processing step is applied to candidate corner points identified by the quantum circuit. Results show that the proposed quantum circuits produce outputs consistent with classical Sobel and Harris operators. Furthermore, the QPIE-based configuration yields more stable and coherent results than FRQI, especially under limited measurement shots. While gradient computation can be performed efficiently at the circuit level, the overall cost remains dominated by state preparation, measurement, and classical post-processing. All experiments are conducted under noiseless simulation, and performance on NISQ hardware may be affected by noise and measurement limitations. Therefore, this work demonstrates a functional and scalable quantum realization of classical edge and corner detection methods rather than an end-to-end speedup.