Differentiable Logical Programming for Quantum Circuit Discovery and Optimization

• URL: http://arxiv.org/abs/2602.08880v1
• Date: Mon, 09 Feb 2026 16:40:19 GMT
• Title: Differentiable Logical Programming for Quantum Circuit Discovery and Optimization
• Abstract summary: We introduce a neuro-symbolic framework that reframes quantum circuit design as a differentiable logic programming problem.<n>Our model represents a scaffold of potential quantum gates and parameterized operations as a set of learnable, continuous truth values''<n>We report a hardware-aware adaptation experiment on the 133-qubit IBM Torino processor.
• Score: 0.15229257192293197
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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,'' $s \in [0, 1]^N$. 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 a hardware-aware adaptation experiment on the 133-qubit IBM Torino processor, where the method improved fidelity by 59.3 percentage points in a localized routing task while adapting to hardware failures.

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