Do Quantum AIs Dream in Paths? Path-Integral Slow Thinking through Grover Interference
Abstract
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.
Related
- Harmonic Reduction of Spin-Coupled Grover Walks on Hypercubes via Quantum Bernoulli Noises
- Depth analysis of the Quantum Approximate Optimization Algorithm with a Grover mixer
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- One-Shot and Concurrent Hitting Times for Grover-Coined Quantum Walks on Cubelike Graphs
BibTeX
@misc{cai2026quantum,
title = {{Do Quantum AIs Dream in Paths? Path-Integral Slow Thinking through Grover Interference}},
author = {Xiansheng Cai and Xiu-Hao Deng and Kun Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05842},
eprint = {2609.05842},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05842},
}
RIS
TY - UNPB
TI - Do Quantum AIs Dream in Paths? Path-Integral Slow Thinking through Grover Interference
AU - Xiansheng Cai
AU - Xiu-Hao Deng
AU - Kun Chen
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.05842
UR - https://arxiv.org/abs/2609.05842
AB - 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.
ER -