# Differentiable Logical Programming for Quantum Circuit Discovery and Optimization

arXiv: https://arxiv.org/abs/2602.08880 · HTML: https://mlsanity.com/paper/2602.08880/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 24 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 6 of 6)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Curriculum reinforcement learning for quantum architecture search under hardware errors](https://mlsanity.com/paper/2402.03500/) (2024)
- [TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search](https://mlsanity.com/paper/2505.09371/) (2025)

## Abstract (arXiv)

Designing high-fidelity quantum circuits remains challenging, and current paradigms often depend on heuristic, fixed-ansatz structures or rule-based compilers that can be suboptimal or lack generality. We introduce a neuro-symbolic framework that reframes quantum circuit design as a differentiable logic programming problem. Our model represents a scaffold of potential quantum gates and parameterized operations as a set of learnable, continuous ``truth values'' or ``switches,'' s ∈ [0, 1]N. These switches are optimized via standard gradient descent to satisfy a user-defined set of differentiable, logical axioms (e.g., correctness, simplicity, robustness). We provide a theoretical formulation bridging continuous logic (via T-norms) and unitary evolution (via geodesic interpolation), while addressing the barren plateau problem through biased initialization. We illustrate the approach on tasks including discovery of a 4-qubit Quantum Fourier Transform (QFT) from a scaffold of 21 candidate gates. We also report hardware-aware adaptation experiments on the 156-qubit IBM Fez processor, where the method autonomously adapted to both gradual noise drift (24.2~pp over static baseline) and catastrophic hardware failure (46.7~pp post-failure improvement), using only measurement-driven gradient updates with no hardwired bias or prior path preference