arXiv subjects

Osama Muhammad Raisuddin

Publications and source records attributed to Osama Muhammad Raisuddin.

5 recordsLinked to original sources

arXiv2025

Quantum-Assisted Vehicle Routing: Realizing QAOA-based Approach on Gate-Based Quantum Computer

The Vehicle Routing Problem (VRP) is a fundamental combinatorial optimization challenge with broad applications in logistics and transportation. In this work, we present a quantum-assisted framework that integrates the Quantum Approximate Optimization Algorithm (QAOA) with a link-based formulation of VRP. Our approach encodes flow conservation and subtour elimination directly into the cost Hamiltonian, preserving graph structure while minimizing resource requirements for practical hardware implementation. We design and implement the full pipeline on a gate-based quantum computer, including problem formulation, encoding, circuit synthesis, and execution on IBM Quantum System One. Experimental results on small VRP instances highlight the effects of penalty scaling, coefficient normalization, and circuit depth on solution feasibility under hardware noise. While scalability remains constrained by circuit complexity and decoherence, the study demonstrates a practical pathway for implementing VRP on quantum hardware and identifies methodological directions for advancing near-term quantum optimization.

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arXiv2024

A Review of Quantum Scientific Computing Algorithms for Engineering Problems

Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering applications. This advancement presents both opportunities and challenges, requiring engineers to familiarize themselves with quantum principles, applications, and complexities. This paper systematically explores the foundational concepts of quantum mechanics and their implications for computational advancements, emphasizing the superiority of quantum algorithms in solving engineering problems. It identifies areas where gate-based quantum computing has the potential to outperform classical methods despite facing scalability and coherence issues. By offering clear examples with minimal reliance on in-depth quantum physics or hardware specifics, the aim is to make quantum computing accessible to engineers, addressing the steep learning curve and fostering its practical adoption for complex problem-solving and technological advancement as quantum hardware becomes more robust and reliable.

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arXiv2024

Quantum Multigrid Algorithm for Finite Element Problems

Quantum linear system algorithms (QLSAs) can provide exponential speedups for the solution of linear systems, but the growth of the condition number for finite element problems can eliminate the exponential speedup. QLSAs are also incapable of using an initial guess of a solution to improve upon it. To circumvent these issues, we present a Quantum Multigrid Algorithm (qMG) for the iterative solution of linear systems by applying the sequence of multigrid operations on a quantum state. Given an initial guess with error e_0, qMG can produce a vector encoding the entire sequence of multigrid iterates with the final iterate having a relative error e'=e/e_0, as a subspace of the final quantum state, with exponential advantage in O( poly log (N/e') ) time using O( poly log (N/e') ) qubits. Although extracting the final iterate from the sequence is efficient, extracting the sequence of iterates from the final quantum state can be inefficient. We provide an analysis of the complexity of the method along with numerical analysis.

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arXiv2023

Quantum Relaxation for Linear Systems in Finite Element Analysis

Quantum linear system algorithms (QLSAs) for gate-based quantum computing can provide exponential speedups for solving linear systems but face challenges when applied to finite element problems due to the growth of the condition number with problem size. Furthermore, QLSAs cannot use an approximate solution or initial guess to output an improved solution. Here, we present Quantum Relaxation for Linear System (qRLS), as an iterative approach for gate-based quantum computers by embedding linear stationary iterations into a larger block linear system. The condition number of the block linear system scales linearly with the number of iterations independent of the size and condition number of the original system. The well-conditioned system enables a practical iterative solution of finite element problems using the state-of-the-art Quantum Signal Processing (QSP) variant of QLSAs, for which we provide numerical results using a quantum computer simulator. The iteration complexity demonstrates favorable scaling relative to classical architectures, as the solution time is independent of system size and requires O(log(N)) qubits. This represents an exponential efficiency gain, offering a new approach for iterative finite element problem-solving on quantum hardware.

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arXiv2022

FEqa: Finite Element Computations on Quantum Annealers

The solution of physical problems discretized using the finite element methods using quantum computers remains relatively unexplored. Here, we present a unified formulation (FEqa) to solve such problems using quantum annealers. FEqa is a hybrid technique in which the finite element problem is formulated on a classical computer, and the residual is minimized using a quantum annealer. The advantages of FEqa include utilizing a single qubit per degree of freedom, enforcing Dirichlet boundary conditions a priori, reaching arbitrary solution precision, and eliminating the possibility of the annealer generating invalid results. FEqa is scalable on the classical portion of the algorithm due to its Single Program Multiple Data (SPMD) nature and does not rely on ground state solutions from the annealer. The exponentially large number of collocation points used in quantum annealing are investigated for their cosine measures, and new iterative techniques are developed to exploit their properties. The quantum annealer has clear advantages in computational time over simulated annealing, for the example problems presented in this paper solved on the D-Wave machine. The presented work provides a pathway to solving physical problems using quantum annealers.

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