# Position: Quantum Program Generation Must Prioritize Validity Over Probabilistic Scaling

arXiv: https://arxiv.org/abs/2607.15313 · HTML: https://mlsanity.com/paper/2607.15313/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 64 references that are in the map.
- First posted on arXiv 15 Jul 2026.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [PICARD: Parsing Incrementally for Constrained Auto-Regressive Decoding from Language Models](https://mlsanity.com/paper/2109.05093/) (2021)
- [Grounded Copilot: How Programmers Interact with Code-Generating Models](https://mlsanity.com/paper/2206.15000/) (2022)
- [Inverse Scaling: When Bigger Isn't Better](https://mlsanity.com/paper/2306.09479/) (2023)
- [LLMs Can't Plan, But Can Help Planning in LLM-Modulo Frameworks](https://mlsanity.com/paper/2402.01817/) (2024)
- [A Closer Look at Invalid Action Masking in Policy Gradient Algorithms](https://mlsanity.com/paper/2006.14171/) (2020)
- [Constrained Language Models Yield Few-Shot Semantic Parsers](https://mlsanity.com/paper/2104.08768/) (2021)
- [A Large-Scale Survey on the Usability of AI Programming Assistants: Successes and Challenges](https://mlsanity.com/paper/2303.17125/) (2023)
- [Large Language Models for Compiler Optimization](https://mlsanity.com/paper/2309.07062/) (2023)
- [Inverse Scaling in Test-Time Compute](https://mlsanity.com/paper/2507.14417/) (2025)
- [Quantum Circuit Optimization with AlphaTensor](https://mlsanity.com/paper/2402.14396/) (2024)
- [APOLLO: Automated LLM and Lean Collaboration for Advanced Formal Reasoning](https://mlsanity.com/paper/2505.05758/) (2025)
- [Qiskit HumanEval: An Evaluation Benchmark For Quantum Code Generative Models](https://mlsanity.com/paper/2406.14712/) (2024)
- [The Larger They Are, the Harder They Fail: Language Models do not Recognize Identifier Swaps in Python](https://mlsanity.com/paper/2305.15507/) (2023)
- [Qiskit Code Assistant: Training LLMs for generating Quantum Computing Code](https://mlsanity.com/paper/2405.19495/) (2024)
- [Assessing requirements to scale to practical quantum advantage](https://mlsanity.com/paper/2211.07629/) (2022)
- [Testing and Debugging Quantum Programs: The Road to 2030](https://mlsanity.com/paper/2405.09178/) (2024)
- [Don't Panic! Better, Fewer, Syntax Errors for LR Parsers](https://mlsanity.com/paper/1804.07133/) (2018)
- [Algorithmic Theory of Qubit Routing](https://mlsanity.com/paper/2305.02059/) (2023)
- [An Evaluation Benchmark for Autoformalization in Lean4](https://mlsanity.com/paper/2406.06555/) (2024)
- [Succinct Classical Verification of Quantum Computation](https://mlsanity.com/paper/2206.14929/) (2022)
- [SAIS: A Novel Bio-Inspired Artificial Immune System Based on Symbiotic Paradigm](https://mlsanity.com/paper/2402.07244/) (2024)

## Abstract (arXiv)

The scaling hypothesis assumes that increasing model parameters yields emergent reasoning capabilities. This position paper argues that applying this probabilistic paradigm to generic quantum circuit synthesis is a directional error. Unlike natural languages, quantum circuits require strict adherence to mathematical constraints that manifest a significant syntax-semantics gap. Training on unverified quantum programs means that models learn syntax but fail to capture the physical semantics of the Hilbert space. Since the valid subset of circuit designs decays exponentially with the number of qubits, post-hoc filtering is mathematically intractable. We propose a pivot from human-centric copilots to verifier-centric agents. We integrate hierarchical constraints, topological masks, and symbolic proxies directly into generation. Our analysis suggests that scale alone cannot bridge the validity gap. Verification-aware architectures offer a viable path for modular quantum program generation. These considerations point toward generation methods that encode task-specific rules of quantum information, rather than relying on imitation alone.