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Integrating Quantum Circuit Reasoning into Large-Scale Neurosymbolic AI Architectures

Andrew Kiruluta

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.13140/rg.2.2.19289.17766

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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 γγγ. 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.
Variational quantum circuits (VQCs) constitute a central building block of near-term quantum machine learning (QML), yet the principled design of expressive and trainable architectures remains a major open challenge. The VQC design space grows combinatorially with the number of qubits, layers, entanglement structures, and gate parameterizations, rendering manual circuit construction inefficient and often suboptimal. We introduce an autonomous agent-based framework for VQC architecture search that integrates high-level reasoning with a quantum simulation environment. The agent proposes candidate circuit architectures, evaluates them through fully automated training and validation pipelines, and iteratively improves its design strategy via performance-driven feedback. Empirically, we show that the agent autonomously evolves circuit architectures from simple initial ansätze toward increasingly expressive designs, progressively trying to improve task performance. This demonstrates that agentic AI can effectively navigate and refine the VQC design landscape with minimal human intervention, providing a scalable methodology for automated quantum model development in the Noisy Intermediate-Scale Quantum (NISQ) regime.
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We introduce DeepQuantum, an open-source, PyTorch-based software platform for quantum machine learning and photonic quantum computing. This AI-enhanced framework enables efficient design and execution of hybrid quantum-classical models and variational quantum algorithms on both CPUs and GPUs. For photonic quantum computing, DeepQuantum implements Fock, Gaussian, and Bosonic backends, catering to different simulation needs. To our knowledge, it is the first framework to realize closed-loop integration of three paradigms of quantum computing, namely quantum circuits, photonic quantum circuits, and measurement-based quantum computing, thereby enabling robust support for both specialized and universal photonic quantum algorithm design. Furthermore, DeepQuantum supports large-scale simulations based on tensor network techniques and a distributed parallel computing architecture. We demonstrate these capabilities through comprehensive benchmarks and illustrative examples. With its unique features, DeepQuantum is intended to be a powerful platform for both AI for Quantum and Quantum for AI.