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Differentiable Logical Programming for Quantum Circuit Discovery and Optimization

arXiv 2602.08880 ↗First posted 9 Feb 2026quant-ph cs.LGcited by 0

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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

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.

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6 of 24 references.

References · 6

  1. 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,739
  2. 2018DARTS: Differentiable Architecture Searchcited by 1,798
  3. 2016The Concrete Distribution: A Continuous Relaxation of Discrete Random Variablescited by 1,148
  4. 2018Barren plateaus in quantum neural network training landscapescited by 630
  5. 2024Curriculum reinforcement learning for quantum architecture search under hardware errorscited by 37
  6. 2025TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture searchcited by 7

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  3. 2024Differentiable Quantum Architecture Search in Asynchronous Quantum Reinforcement Learning
  4. 2026Beyond Reinforcement Learning: Fast and Scalable Quantum Circuit Synthesis
  5. 2025Agent-Q: Fine-Tuning Large Language Models for Quantum Circuit Generation and Optimization
  6. 2026Differentiable Logic Synthesis: Spectral Coefficient Selection via Sinkhorn-Constrained Composition
  7. 2025Separating Ansatz Discovery from Deployment on Larger Problems: Reinforcement Learning for Modular Circuit Design
  8. 2024Practical and efficient quantum circuit synthesis and transpiling with Reinforcement Learning