SCALAR: A Neurosymbolic Framework for Automated Conjecture and Reasoning in Quantum Circuit Analysis

2026-05-11

AI Summary

This work addresses the challenge of interpreting the relationship between parameters and graph structure in the Quantum Approximate Optimization Algorithm (QAOA) by introducing the first neurosymbolic system tailored for quantum circuit analysis. The proposed framework integrates the CUDA-Q tensor network simulator, symbolic regression, and large language model reasoning to establish a closed loop from data-driven hypothesis generation to symbolic explanation. Evaluated on 82 MaxCut instances and 2,000 random graphs, the method not only reproduces known parameter transfer phenomena but also uncovers novel correlations between QAOA parameters and graph invariants. Furthermore, it successfully scales to 77 qubits, revealing previously unknown connections between graph topology and the optimization landscape.

Abstract

In this paper, we present SCALAR (Symbolic Conjecture and LLM-Assisted Reasoning), a neurosymbolic framework for automated conjecture generation in quantum circuit analysis built on top of the CUDA-Q open source framework. The system integrates quantum simulation, symbolic conjecture generation, and LLM-based interpretation. We evaluate SCALAR on 82 MaxCut instances from the MQLib benchmark dataset and extend the analysis to 2,000 randomly generated graphs across four topologies: regular, Erdos-Renyi, Barabasi-Albert, and Watts-Strogatz. The framework generates conjectured bounds relating optimal QAOA parameters to graph invariants, including known relationships such as periodicity constraints on the phase separation parameter $γ$. SCALAR also recovers previously reported parameter transfer phenomena across structurally similar instances. Additionally, the system identifies correlations between graph structural features and optimization landscape properties, which we characterize through invariant-based descriptors. Using CUDA-Q tensor network simulator, we scale experiments to instances of up to 77 qubits. We discuss the accuracy, generality, and limitations of the generated conjectures, including sensitivity to graph class and quantum circuit depth.

Problem

• quantum circuit analysis
• conjecture generation
• QAOA parameters
• graph invariants
• optimization landscape

Innovation

• neurosymbolic reasoning
• automated conjecture generation
• quantum circuit analysis
• QAOA parameter optimization
• graph invariants