arXiv subjects

Abdelmouheymen Rabah Khamadja

Publications and source records attributed to Abdelmouheymen Rabah Khamadja.

3 recordsLinked to original sources

arXiv2026

Probing the Ground State of the Antiferromagnetic Heisenberg Model on the Kagome Lattice using Geometrically Informed Variational Quantum Eigensolver

This work investigates the nature of the ground state of the antiferromagnetic Heisenberg model on fundamental kagome cells, a triangle and a star, using the variational quantum eigensolver (VQE) algorithm on real quantum hardware. We demonstrate that the ground state preparation is achievable using a shallow hardware-efficient quantum circuit with a naturally Euclidean parameter space. Our custom ansatz is capable of accurately recovering meaningful properties of the ground state such as the spin-spin correlation terms and static structure factor without explicit error mitigation. These features are found to be resilient to noise. We exploited the Fubini-Study metric in constructing the ansatz, ensuring a singularity-free parameter space. With this ansatz design, the adaptive gradient descent optimizer achieves a faster convergence in terms of the number of iterations compared to simultaneous perturbation stochastic approximation (SPSA). We further apply error mitigation techniques, including zero-noise extrapolation (ZNE) and qubit-wise readout error mitigation (REM). While ZNE does not obey the Rayleigh-Ritz variational principle, the conditions under which REM preserves it are discussed.

quant-ph↗

arXiv2025

From VQE To SQD: Modern Quantum Algorithms For The Electronic Structure Problem

This thesis investigates sampling-based quantum algorithms for electronic ground state energy estimation, focusing on Quantum-Selected Configuration Interaction (QSCI) and Sample-Based Quantum Diagonalization (SQD) as near-term alternatives to the Variational Quantum Eigensolver (VQE). Unlike VQE, which suffers from barren plateaus and high measurement costs, these methods avoid variational optimization by sampling Slater determinants from quantum hardware and performing diagonalization classically. The central contribution is the first analytical expression for the sampling bottleneck: the determinant-discovery step is mapped to the classical coupon-collector problem, yielding both an exact formula and a scalable lower-bound estimator for the number of measurements required to recover all determinants contributing to the ground state. Previous work only relied on numerical sampling and estimation. The analysis is validated through simulations, hardware-calibrated noisy studies, and execution on IBM's 127-qubit IBM Brisbane processor, demonstrating the dominant role of sampling efficiency in the near-term feasibility of QSCI and SQD. This work was carried out under the supervision of Dr. Mohamed Taha Rouabah.

quant-ph↗

arXiv2025

Improving VQE Parameter Quality on Noisy Quantum Processors with Cost-Effective Readout Error Mitigation

The inherent noise in current Noisy Intermediate-Scale Quantum (NISQ) devices presents a major obstacle to the accurate implementation of quantum algorithms such as the Variational Quantum Eigensolver (VQE) for quantum chemistry applications. This study examines the impact of error mitigation strategies on VQE performance. We show that, for small molecular systems, an older-generation 5-qubit quantum processing unit (IBMQ Belem), when combined with optimized Twirled Readout Error Extinction (T-REx), achieves ground-state energy estimations an order of magnitude more accurate than those obtained from a more advanced 156-qubit device (IBM Fez) without error mitigation. Our findings demonstrate that T-REx, a computationally inexpensive error mitigation technique, substantially improves VQE accuracy not only in energy estimation, but more importantly in optimizing the variational parameters that characterize the molecular ground state. Consequently, state-vector simulated energies suggest that the accuracy of the optimized variational parameters provides a more reliable benchmark of VQE performance than quantum hardware energy estimates alone. Our results point to the critical role of error mitigation in extending the utility of noisy quantum hardware for molecular simulations.

quant-ph↗