# CARVE-Q: Quantum-Proposed, Classically Certified Interactive Driving Repair

arXiv: https://arxiv.org/abs/2606.06531 · HTML: https://mlsanity.com/paper/2606.06531/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 14 of 14)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles](https://mlsanity.com/paper/1604.07446/) (2016)
- [INTERACTION Dataset: An INTERnational, Adversarial and Cooperative moTION Dataset in Interactive Driving Scenarios with Semantic Maps](https://mlsanity.com/paper/1910.03088/) (2019)
- [Convolutional Social Pooling for Vehicle Trajectory Prediction](https://mlsanity.com/paper/1805.06771/) (2018)
- [Multi-Agent Pathfinding: Definitions, Variants, and Benchmarks](https://mlsanity.com/paper/1906.08291/) (2019)
- [On a Formal Model of Safe and Scalable Self-driving Cars](https://mlsanity.com/paper/1708.06374/) (2017)
- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [TensorFlow Quantum: A Software Framework for Quantum Machine Learning](https://mlsanity.com/paper/2003.02989/) (2020)
- [Lifelong Multi-Agent Path Finding for Online Pickup and Delivery Tasks](https://mlsanity.com/paper/1705.10868/) (2017)
- [LaCAM: Search-Based Algorithm for Quick Multi-Agent Pathfinding](https://mlsanity.com/paper/2211.13432/) (2022)
- [Liability, Ethics, and Culture-Aware Behavior Specification using Rulebooks](https://mlsanity.com/paper/1902.09355/) (2019)

## Abstract (arXiv)

The critical question after a correct driving veto is not only whether a maneuver is unsafe, but whether the blocked interaction admits a lawful, auditable, and responsibility-bounded repair. Prediction and game-theoretic planners can suggest plausible cooperation, yet they do not return a proof that the repair respects hard rules, right-of-way, cost allocation, and ego fallback. We introduce CARVE, Certified Affordable Repair of Vetoed maneuvers via Envelopes, a certificate architecture for prediction-free interactive repair. Given a vetoed maneuver, CARVE constructs a finite repair lattice and emits a structured certificate recording the binding rule, selected joint repair, right-of-way-scaled cooperation envelope, responsibility-weighted cost split, and ego-only fallback. This certificate view reveals the algorithmic bottleneck: multi-owner repair induces a product lattice M = prodj |Aj|. We therefore introduce CARVE-Q, a verifier-shielded quantum-AI search layer that applies quantum minimum finding only to this black-box lattice while leaving all safety authority classical. In the conservative verifier-oracle model, exact classical minimum finding requires Theta(M) queries in the worst case, whereas Durr-Hoyer/Grover minimum finding uses O(√M) oracle queries with high probability. We prove verifier-shielded certificate soundness, priority non-elicitation, black-box query separation, and finite-precision reversible-oracle constructibility. We then demonstrate state-vector minimum finding on CARVE repair oracles up to 65,536 assignments and validate certificate preservation on Lanelet2-grounded INTERACTION replay with 100% right-of-way respect, 100% blame consistency, and zero priority false positives. The result is a trust-bounded quantum-AI pattern for certified autonomy: quantum proposes; CARVE certifies.