用复数相位在圆上计算，实现轻量级类量子算法
PhasorFlow: A Python Library for Unit Circle Based Computing
- 将输入编码为复数相位，通过单位酉门进行连续几何梯度计算
- 提出可训练的相位电路模型，支持金融波动检测等新任务
- 无需参数的傅里叶注意力层，适合经典硬件上的高效推理
我们提出 PhasorFlow，一个开源的 Python 库，用于在 $S^1$ 单位圆上进行计算。输入以复数相位 $z=e^{iϕ}$ 形式编码于 $N$-环面 ($\mathbb{T}^N$)；随着计算通过酉波干涉门进行，全局范数保持不变，而分量漂移至 $\mathbb{C}^N$，使算法能利用连续几何梯度。PhasorFlow 有三项贡献：第一，形式化了相位电路模型（$N$ 线程，$M$ 门），并提供包含标准酉、非线性、神经形态和编码操作的 22 种门库，支持完整矩阵代数模拟；第二，引入变分相位电路（VPC），一种类似变分量子电路的原生相位分类器；第三，提出相位变换器模块与大相位模型（LPM），以无参数 DFT 令牌混合层替代 $QK^TV$ 注意力。我们在金融波动检测、神经形态联想记忆、神经绑定、周期发现及算法逻辑等独特任务上验证了该框架。这使得单位圆计算成为一种确定性、轻量级的经典硬件范式。代码地址：https://github.com/mindverse-computing/phasorflow。
原文摘要 · Abstract (English)
We present PhasorFlow, an open-source Python library for computing on the $S^1$ unit circle. Inputs are encoded as complex phasors $z=e^{iϕ}$ on the $N$-torus ($\mathbb{T}^N$); as computation proceeds through unitary wave-interference gates, global norm is preserved while components drift into $\mathbb{C}^N$, letting algorithms leverage continuous geometric gradients. PhasorFlow makes three contributions. First, we formalize the Phasor Circuit model ($N$ threads, $M$ gates) with a 22-gate library spanning standard-unitary, non-linear, neuromorphic, and encoding operations under full matrix-algebra simulation. Second, we introduce the Variational Phasor Circuit (VPC), a trainable phase-native classifier analogous to variational quantum circuits. Third, we introduce the Phasor Transformer block and Large Phasor Model (LPM), replacing $QK^TV$ attention with a parameter-free DFT token-mixing layer. We validate the framework on financial volatility detection, neuromorphic associative memory, neural binding, period finding, and algorithmic logic applications that are unique to the library. This positions unit-circle computing as a deterministic, lightweight paradigm on classical hardware. Available at https://github.com/mindverse-computing/phasorflow.
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