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

• URL: http://arxiv.org/abs/2605.10327v1
• Date: Mon, 11 May 2026 10:31:18 GMT
• Title: SCALAR: A Neurosymbolic Framework for Automated Conjecture and Reasoning in Quantum Circuit Analysis
• Abstract summary: We present SCALAR, a neurosymbolic framework for automated conjecture generation in quantum circuit analysis.<n>The system integrates quantum simulation, symbolic conjecture generation, and LLM-based interpretation.<n>We discuss the accuracy, generality, and limitations of the generated conjectures, including sensitivity to graph class and quantum circuit depth.
• Score: 1.5084818199355905
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• GroverFigureOfMerit: An Agnostic Figure of Merit for Quantum Backend Characterization in the NISQ Era [41.99844472131922]
  We propose a Figure of Merit based on Grover's algorithm as an algorithmic stress test evaluating quantum backend performance holistically.<n>The metric combines success probability on target states with penalties for non-uniform amplification and leakage to non-marked states, yielding a unified score across hardware architectures.
  arXiv  Detail & Related papers  (2026-07-09T16:08:48Z)
• Continual Quantum Architecture Search with Tensor-Train Encoding: Theory and Applications to Signal Processing [68.35481158940401]
  CL-QAS is a continual quantum architecture search framework.<n>It mitigates challenges of costly encoding amplitude and forgetting in variational quantum circuits.<n>It achieves controllable robustness expressivity, sample-efficient generalization, and smooth convergence without barren plateaus.
  arXiv  Detail & Related papers  (2026-01-10T02:36:03Z)
• Performance Guarantees for Quantum Neural Estimation of Entropies [31.955071410400947]
  Quantum neural estimators (QNEs) combine classical neural networks with parametrized quantum circuits.<n>We study formal guarantees for QNEs of measured relative entropies in the form of non-asymptotic error risk bounds.<n>Our theory aims to facilitate principled implementation of QNEs for measured relative entropies.
  arXiv  Detail & Related papers  (2025-11-24T16:36:06Z)
• SPD Learning for Covariance-Based Neuroimaging Analysis: Perspectives, Methods, and Challenges [41.955864444491965]
  Neuroimaging provides a critical framework for characterizing brain activity by quantifying connectivity patterns and functional architecture across modalities.<n>Modern machine learning has significantly advanced our understanding of neural processing mechanisms through these datasets.<n>This review focuses on machine learning approaches for covariance-based neuroimaging data, where often symmetric positive definite (SPD) matrices under full-rank conditions encode inter-channel relationships.
  arXiv  Detail & Related papers  (2025-04-26T10:05:04Z)
• Communities in the Kuramoto Model: Dynamics and Detection via Path Signatures [1.024113475677323]
  We propose the use of path signatures, a mathematical framework that encodes geometric and temporal properties of continuous paths.<n>We propose a novel signature-based community detection algorithm, achieving exact recovery of structural communities from observed time series.<n>Our results demonstrate that path signatures provide a novel perspective on analyzing complex neural data and other high-dimensional systems.
  arXiv  Detail & Related papers  (2025-03-21T21:41:48Z)
• Exact Computation of Any-Order Shapley Interactions for Graph Neural Networks [53.10674067060148]
  Shapley Interactions (SIs) quantify node contributions and interactions among multiple nodes.<n>By exploiting the GNN architecture, we show that the structure of interactions in node embeddings are preserved for graph prediction.<n>We introduce GraphSHAP-IQ, an efficient approach to compute any-order SIs exactly.
  arXiv  Detail & Related papers  (2025-01-28T13:37:44Z)
• Quantum walk informed variational algorithm design [0.0]
  We present a theoretical framework for the analysis of amplitude transfer in Quantum Variational Algorithms (QVAs) We develop algorithms for unconstrained and constrained novel optimisations. We show significantly improved convergence over preexisting QVAs.
  arXiv  Detail & Related papers  (2024-06-17T15:04:26Z)
• Unifying (Quantum) Statistical and Parametrized (Quantum) Algorithms [65.268245109828]
  We take inspiration from Kearns' SQ oracle and Valiant's weak evaluation oracle. We introduce an extensive yet intuitive framework that yields unconditional lower bounds for learning from evaluation queries.
  arXiv  Detail & Related papers  (2023-10-26T18:23:21Z)
• Sequential measurements, TQFTs, and TQNNs [0.0]
  We introduce novel methods for implementing generic quantum information within a scale-free architecture. We show how observational outcomes are taken to be finite bit strings induced by measurement operators derived from a holographic screen bounding the system. We extend the analysis so develop topological quantum neural networks (TQNNs), which enable machine learning with functorial evolution of quantum neural 2-complex quiveres.
  arXiv  Detail & Related papers  (2022-05-26T06:37:57Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)
• Chaos and Complexity from Quantum Neural Network: A study with Diffusion Metric in Machine Learning [0.0]
  We study the phenomena of quantum chaos and complexity in the machine learning dynamics of Quantum Neural Network (QNN) We employ a statistical and differential geometric approach to study the learning theory of QNN.
  arXiv  Detail & Related papers  (2020-11-16T10:41:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.