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

arXiv: https://arxiv.org/abs/2605.10327 · HTML: https://mlsanity.com/paper/2605.10327/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 10 of its 32 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 10 of 10)

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Quantum Architecture Search: A Survey](https://mlsanity.com/paper/2406.06210/) (2024)
- [Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the ErdHos Problems](https://mlsanity.com/paper/2601.22401/) (2026)
- [Mathematical conjecture generation using machine intelligence](https://mlsanity.com/paper/2306.07277/) (2023)
- [Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects](https://mlsanity.com/paper/2407.00736/) (2024)
- [QAOA-GPT: Efficient Generation of Adaptive and Regular Quantum Approximate Optimization Algorithm Circuits](https://mlsanity.com/paper/2504.16350/) (2025)
- [Classical symmetries and the Quantum Approximate Optimization Algorithm](https://mlsanity.com/paper/2012.04713/) (2020)
- [Q-Fusion: Diffusing Quantum Circuits](https://mlsanity.com/paper/2504.20794/) (2025)
- [Theoretical Approximation Ratios for Warm-Started QAOA on 3-Regular Max-Cut Instances at Depth p=1](https://mlsanity.com/paper/2402.12631/) (2024)

## Abstract (arXiv)

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.