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

TL;DR

SCALAR is a neurosymbolic framework that automates conjecture generation and reasoning in quantum circuit analysis, leveraging quantum simulation, symbolic methods, and language models to analyze diverse graph instances.

Contribution

The paper introduces SCALAR, a novel neurosymbolic system that automates conjecture generation in quantum circuit analysis, integrating simulation, symbolic reasoning, and LLMs.

Findings

Successfully generated conjectured bounds relating QAOA parameters to graph invariants.

Recovered known parameter transfer phenomena across similar graph instances.

Scalable to quantum circuits with up to 77 qubits using CUDA-Q tensor network simulator.

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 $\gamma$. 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.