MPS-JuliQAOA: User-Friendly, Scalable MPS-Based Simulation for Quantum Optimization

We present MPS-JuliQAOA, an open-source, Julianative framework for simulating the Quantum Approximate Optimization Algorithm (QAOA) using Matrix Product States (MPS). The tool supports general cost Hamiltonians that are diagonal in the computational basis and integrates tensornetwork simulation with automatic differentiation for parameter optimization within a unified workflow. Built on the ITensor ecosystem, MPS-JuliQAOA replaces exact statevector simulation with an MPS backend, enabling QAOA simulations beyond the practical limits of full statevector methods when entanglement growth remains controlled. We demonstrate simulations of up to 512 qubits and 20 QAOA layers on 3-regular Max-Cut instances, and analyze runtime scaling and approximation accuracy as functions of bond dimension and circuit depth. The framework abstracts tensor-network and differentiation details from the user, allowing high-level Hamiltonian specification without requiring expertise in MPS methods. Source code is publicly available at https://github.com/lanl/JuliQAOA.jl/tree/mps.