摘要
arXiv:2603.15886v3 Announce Type: replace-cross Abstract: We present PhasorFlow, an open-source Python library for computing on the $S^1$ unit circle. Inputs are encoded as complex phasors $z=e^{i\phi}$ 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 present the Variational Phasor Circuit (VPC), analogous to variational quantum circuits, optimizing continuous phase parameters for classification. Third, we introduce the Phasor Transformer, replacing $QK^TV$ attention with a parameter-free DFT token-mixing layer inspired by FNet.