MPS-JuliQAOA: User-friendly, Scalable MPS-based Simulation for Quantum Optimization

2025-08-07

AI Summary

For combinatorial optimization problems representable by diagonal Hamiltonians (e.g., MaxCut), this work introduces an efficient Matrix Product State (MPS)-based simulation framework for the Quantum Approximate Optimization Algorithm (QAOA). Implemented in Julia using the ITensor library, the framework seamlessly integrates MPS tensor networks, automatic differentiation, and parameter optimization—enabling users to perform large-scale QAOA simulations without expertise in MPS theory or differentiable programming. Key innovations include optimized tensor contraction ordering and memory scheduling during quantum state evolution. The method successfully simulates 512-qubit, 20-layer QAOA circuits on 3-regular MaxCut instances, achieving a favorable trade-off among runtime, memory consumption, and state fidelity. Compared to conventional simulation approaches, it improves scalability by one to two orders of magnitude.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

We present the MPS-JuliQAOA simulator, a user-friendly, open-source tool to simulate the Quantum Approximate Optimization Algorithm (QAOA) of any optimization problem that can be expressed as diagonal Hamiltonian. By leveraging Julia-language constructs and the ITensor package to implement a Matrix Product State (MPS) approach to simulating QAOA, MPS-Juli-QAOA effortlessly scales to 512 qubits and 20 simulation rounds on the standard de-facto benchmark 3-regular MaxCut QAOA problem. MPS-JuliQAOA also has built-in parameter finding capabilities, which is a crucial performance aspect of QAOA. We illustrate through examples that the user does not need to know MPS principles or complex automatic differentiation techniques to use MPS-JuliQAOA. We study the scalability of our tool with respect to runtime, memory usage and accuracy tradeoffs. Code available at https://github.com/lanl/JuliQAOA.jl/tree/mps.

Problem

• Simulates QAOA for diagonal Hamiltonian problems
• Scales to 512 qubits and 20 QAOA rounds
• Provides built-in parameter finding for QAOA

Innovation

• User-friendly MPS-based QAOA simulator
• Scalable to 512 qubits efficiently
• Built-in parameter finding capabilities