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

Sean Feeney; Pooja Rao; Andreas Klappenecker; Reuben Tate; Yuri Alexeev; Stefano Mensa; Elica Kyoseva; Stephan Eidenbenz

quant-phMay 11, 2026

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

Authors: Sean Feeney, Pooja Rao, Andreas Klappenecker, Reuben Tate, Yuri Alexeev, Stefano Mensa, Elica Kyoseva, Stephan Eidenbenz

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.

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An LLM System for Autonomous Variational Quantum Circuit Design

Kenya Sakka, Wataru Mizukami, Kosuke Mitarai

Center for Quantum Information and Quantum Biology, The University of Osaka, 1-2 Machikaneyama, Toyonaka 560-0043, Japan · Graduate School of Engineering Science, The University of Osaka 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan

The design of high performing quantum circuits remains largely dependent on human expertise. We introduce an autonomous agentic framework that employs large language models (LLMs) to conduct iterative quantum circuit designs under explicit design constraints. Our system integrates seven components: Exploration, Generation, Discussion, Validation, Storage, Evaluation, and Review. These components form a closed-loop workflow that combines web-based knowledge acquisition, literature-grounded critique, executable code generation, and experimental feedback. We evaluate the framework on two tasks: quantum feature map construction for quantum machine learning and ansatz generation for variational quantum eigensolver applications in quantum chemistry. In image classification benchmarks, the best generated feature map outperforms representative quantum feature maps and, when scaled to larger qubit counts, surpasses the classical radial basis function kernel. In molecular ground state estimation across seven molecules, the generated ansatz attains competitive accuracy with widely used chemically inspired and hardware-efficient constructions while satisfying the imposed scaling constraints. These results establish LLM driven agentic system as a viable paradigm for automated quantum circuit design and illustrate how AI systems can participate in iterative scientific optimization workflows across scientific domains.

Variational Quantum Circuits Quantum Circuit Simulation Quantum Machine Learning Llm-Driven Computational Chemistry Agentic Systems Large Language

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Abstract

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