# Do Quantum AIs Dream in Paths? Path-Integral Slow Thinking through Grover Interference

arXiv: https://arxiv.org/abs/2609.05842 · HTML: https://mlsanity.com/paper/2609.05842/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 41 references that are in the map.
- First posted on arXiv 5 Sep 2026.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Inference-Aware Fine-Tuning for Best-of-N Sampling in Large Language Models](https://mlsanity.com/paper/2412.15287/) (2024)
- [Rethinking Fine-Tuning when Scaling Test-Time Compute: Limiting Confidence Improves Mathematical Reasoning](https://mlsanity.com/paper/2502.07154/) (2025)
- [Learning and Inference on Generative Adversarial Quantum Circuits](https://mlsanity.com/paper/1808.03425/) (2018)
- [Quantum Policy Iteration via Amplitude Estimation and Grover Search -- Towards Quantum Advantage for Reinforcement Learning](https://mlsanity.com/paper/2206.04741/) (2022)
- [Understanding Diversity Collapse in RLVR via the Lens of Overtraining](https://mlsanity.com/paper/2606.15455/) (2026)
- [Emergent Slow Thinking in LLMs as Inverse Tree Freezing](https://mlsanity.com/paper/2509.23629/) (2025)
- [Learning-at-Criticality in Large Language Models for Quantum Field Theory and Beyond](https://mlsanity.com/paper/2506.03703/) (2025)
- [Quantum framework for Reinforcement Learning: Integrating Markov decision process, quantum arithmetic, and trajectory search](https://mlsanity.com/paper/2412.18208/) (2024)
- [Scalable Quantum Reinforcement Learning on NISQ Devices with Dynamic-Circuit Qubit Reuse and Grover Optimization](https://mlsanity.com/paper/2509.16002/) (2025)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards enables large language models to think slowly, but the same training can induce policy collapse: probability concentrates onto a few successful trajectories and exploratory diversity erodes. We ask whether quantum AI can realize slow thinking differently. We formulate slow thinking as coherent dynamics over reasoning trajectories, a discrete path integral in which action sequences coexist in superposition and recombine before measurement. In our trainable realization, an exact verifier partitions the ensemble into collective accepted and rejected components that interfere under Grover amplitude amplification. A finite Grover evolution is maximized when the pre-amplification success probability lies at an analytically determined value below one, so inference itself defines an interior training target and removes the monotonic pressure toward unit success. In exact statevector simulations of a 2x3 sliding puzzle, Grover training reaches accuracy 0.95 on a 32-question training set at one round, against 0.73 for the strongest classical control. On held-out questions specialization has a cost: an untrained uniform policy read out through the same amplification remains the strongest reference on this solution-dense benchmark, and quantum training preserves far more held-out accuracy than classical training - at four rounds with matched circuit applications the two quantum models reach 3.2 and 3.9 times the strongest classical controls. The number of training questions supported by fixed-size policies trained at each amplification budget also grows faster with the budget than with matched classical repetition. These results establish a Grover-based realization of path-integral slow thinking: the interior target preserves exploratory path diversity, and ensemble-level interference converts it into verified performance.