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.

翻译：设计高保真度量子电路仍然具有挑战性，当前范式通常依赖于启发式、固定拟设结构或基于规则的编译器，这些方法可能并非最优或缺乏普适性。我们引入了一种神经符号框架，将量子电路设计重新构建为一个可微分逻辑编程问题。我们的模型将潜在的量子门和参数化操作构成的支架表示为一组可学习的连续“真值”或“开关”，$s \in [0, 1]^N$。这些开关通过标准梯度下降进行优化，以满足用户定义的一组可微分逻辑公理（例如，正确性、简洁性、鲁棒性）。我们提供了一个理论框架，通过T-范数桥接连续逻辑与通过测地线插值实现的幺正演化，同时通过偏置初始化解决贫瘠高原问题。我们在多项任务上展示了该方法，包括从包含21个候选门的支架中发现一个4量子比特的量子傅里叶变换（QFT）电路。我们还报告了在133量子比特的IBM Torino处理器上进行的一项硬件感知适配实验，该方法在局部布线任务中将保真度提高了59.3个百分点，同时适应了硬件故障。