用可微逻辑编程自动发现和优化量子电路，提升精度与适应性。
Differentiable Logical Programming for Quantum Circuit Discovery and Optimization
- 将量子门结构建模为可学习的连续开关，通过梯度下降优化
- 在4比特量子傅里叶变换中从21个候选门中自动发现最优电路
- 可在真实硬件上自适应噪声漂移与故障，无需预设偏好
设计高保真度量子电路仍具挑战性，现有方法常依赖启发式固定结构或规则编译器，存在次优或通用性不足的问题。本文提出一种神经符号框架，将量子电路设计重构为可微逻辑规划问题。模型将潜在量子门与参数化操作表示为一组可学习的连续‘真值’或‘开关’ $s \in [0, 1]^N$，通过标准梯度下降优化以满足用户定义的可微逻辑公理（如正确性、简洁性、鲁棒性）。我们建立了连续逻辑（通过T-范数）与酉演化（通过测地线插值）的理论联系，并通过偏置初始化缓解退化平原问题。在任务中，从21个候选门的骨架中自主发现4比特量子傅里叶变换（QFT）电路。还在156比特的IBM Fez处理器上进行了硬件感知适配实验，方法仅通过测量驱动的梯度更新，在静态基线基础上实现24.2~pp的噪声漂移改善，并在灾难性硬件故障后提升46.7~pp，无需硬编码偏置或先验路径偏好。
原文摘要 · Abstract (English)
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 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
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