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

arXiv: https://arxiv.org/abs/2505.04880 · HTML: https://mlsanity.com/paper/2505.04880/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 38 of its 62 references that are in the map.
- First posted on arXiv 8 May 2025.

## Placed in

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

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [P-Tuning v2: Prompt Tuning Can Be Comparable to Fine-tuning Universally Across Scales and Tasks](https://mlsanity.com/paper/2110.07602/) (2021)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [HuaTuo: Tuning LLaMA Model with Chinese Medical Knowledge](https://mlsanity.com/paper/2304.06975/) (2023)
- [Flex-MoE: Modeling Arbitrary Modality Combination via the Flexible Mixture-of-Experts](https://mlsanity.com/paper/2410.08245/) (2024)
- [Capabilities of Large Language Models in Control Engineering: A Benchmark Study on GPT-4, Claude 3 Opus, and Gemini 1.0 Ultra](https://mlsanity.com/paper/2404.03647/) (2024)
- [Few shot chain-of-thought driven reasoning to prompt LLMs for open ended medical question answering](https://mlsanity.com/paper/2403.04890/) (2024)

## Built on by (most cited first, 2 of 2)

- [Practical Quantum CIM Empowerment via All-Domestic-Core Agentic Large Model](https://mlsanity.com/paper/2605.23934/) (2026)
- [Fine-Tuning Large Language Models for Quantum Reasoning](https://mlsanity.com/paper/2606.21974/) (2026)

## Abstract (arXiv)

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.