Symbolic Analysis of Grover Search Algorithm via Chain-of-Thought Reasoning and Quantum-Native Tokenization

Understanding the high-level conceptual structure of quantum algorithms from their low-level circuit representations is a critical task for verification, debugging, and education. While traditional numerical simulators can calculate output probabilities, they do not explicitly surface the underlying algorithmic logic, such as the function of an oracle or embedded symmetries. In this work, we shift the focus from numerical simulation to symbolic analysis, investigating whether Large Language Models (LLMs) can automatically interpret quantum circuits and articulate their logic in a human-readable format. We introduce GroverGPT+, a model that leverages Chain-of-Thought reasoning and quantum-native tokenization to analyze Grover's search algorithm. We use Grover's algorithm as a controlled testbed, as its well-defined analytical properties allow for rigorous verification of the model's reasoning process. Our primary finding is that GroverGPT+ successfully identifies the oracle and its marked states directly from circuit representations. The model's key output is not a final probability, but a structured, interpretable reasoning trace that mirrors human expert analysis, effectively translating procedural circuit steps into conceptual insights. Furthermore, we establish a structured benchmark for this symbolic analysis task and explore its empirical extrapolation describing the model's performance as the number of qubits increases. These findings position LLMs as powerful tools for automated quantum algorithm analysis and verification. More fundamentally, this work offers a first step towards using such models as scientific probes, suggesting that an algorithm's ``learnability" by a classical model can provide a new, complementary perspective on its conceptual complexity, a topic of core interest to quantum information science.