Gate Model Quantum Optimization in Multi-Commodity Network Flow Problems

Abstract

This study explores quantum computing for multi-commodity network flow optimiza tion. It effectively distributes diverse commodities along a network while taking con straints and objectives into account. In the quantum approach, qubits represent nodes, quantum gates construct the problem Hamiltonian by combining Hadamard and parametrized Pauli-X gates that leverages superposition and handles edge weights respectively. CNOT gates signify commodity flows, utilizing qubit entanglement. The mixer Hamiltonian’s Pauli-Z gates, modulated for strength, balance exploration and exploitation. The objective function, encapsu lated in these Hamiltonians, drives the quantum circuit’s execution. Post-processing, like filtering and amplification, enhances reliability with the integration of COBYLA optimizer that refines circuit parameters. This study explores 3- to 5-node topologies with 17 variations accommodating even number of commodities. A notable aspect of this work’s novelty is the ingenuous mapping of the problem to quantum circuits, leveraging qubits and strategic gate use, offering a pioneering solution to complex com binatorial challenges through quantum computing. Keywords: Multicommodity Network Flow Quantum Computing, Quantum Optimiza tion, Quantum Algorithms, Variational Quantum Eigensolver (VQE), Quantum Ap proximate Optimization Algorithm (QAOA), Quantum Circuit, Quantum Superposi tion, Quantum Entanglement, Problem Hamiltonian, Mixer Hamiltonian