Distributed Implementation of Variational Quantum Eigensolver to Solve QUBO Problems

We present a distributed algorithm and implementation of the variational quantum eigensolver (VQE), termed distributed VQE (DVQE). DVQE, provided as an open-source Python package, enables the execution of parameterized quantum circuits across multiple logical quantum processing units (QPUs) in a distributed fashion. This approach addresses key hardware limitations of near-term quantum devices, including restricted qubit counts and limited circuit depth. Distributed ansatz circuits are constructed to preserve the quantum state fidelity of their monolithic counterparts, allowing consistent energy estimation while distributing the computational load. To improve the convergence and robustness of the optimization loop for identifying the variational parameters of the DVQE ansatz circuit, we use the ADAM optimizer in combination with metaheuristic initialization strategies, which outperform random initialization across various test cases. The complete DVQE pipeline is implemented in a modular Python package that accepts QUBO problems as input and supports monolithic and distributed execution modes. The framework leverages Qiskit to construct and simulate distributed circuits, and includes an internal greedy algorithm for automatic qubit allocation across multiple QPUs. Simulation results on QUBO benchmarks confirm the correctness of the approach, paving the way for real QPU deployment and further exploration of distributed quantum optimization. \textbf{The simulator is publicly available on \href{https://github.com/LSU-RAISE-LAB/DVQE.git}{GitHub} under a package named raiselab, with a collection of tutorial examples.}